LIBRARY OF CONGRESS, 
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UNITED STATES OF AMERICA. 






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ORGAJSTOJST OF SCIENCE. 



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Three Hooks In One Volume, 



BY 



JOHN IHEAJE&RJC^ON OTlN§ON 9 IS^q:. 




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4 Omnibus has IAterm perlectibvis Sahitein? 



EUREKA, CALIFORNIA: 
Wm. AYRES, BOOK. AND JOB PRINTER, 

107 FIRST STREET, 
1879, 



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^£* 



Entered according to Act of Congress in the year A. D. 1871, b} r 

JOHN HARBISON STINSON, Esq., 

In the office of the Librarian of Congress at Washington, I). 0. 



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PREFACE- 

:o: 

Iq offering a new system of philosophy 1o the scientific world, the 
author is aware that many will say of it at the outset as Omer Pasha did of 
the Alexandrian Library, "If it contain the Koran, we have it already, and 
whatever else it may contain is not worth having." We can only remiud such 
persons that the present age is one of free inquiry, that the human mind at 
best is very feeble and easily deceived by appearances, and that though we 
may be contented and confirmed in our opinions, which are supported by 
the names of distinguished philosophers; yet our condition, perhaps, inay be 
no more happy than that of Pollock's rustic, who w T as confirmed in the belief 
that the visual line which i«irt him round about was the world's extreme. 
Fortunately for the human race, however, there is a class of men in America 
and Europe, whose reflections teach them, that there can be no great advance 
in civilization without an increase of knowledge in science. To such persons 
the author must look for a fair examination of the present work. And in 
calling the attention of seekers after scientific truth in a preface, little more 
can be done by an author than to promise that, in the author's opinion, a 
thorough perusal will repay the reader. 

The thoughts contained in this book have b^cn gained by much labor, 
and have not been set down without much reflection. The subject is a pro- 
found one; and it is, indeed, to the matured philosopher, whose mind has 
been grappling with intricate scientific questions, and who can command and 
concentrate his thoughts, that, in the first instance, the value of new scientific 
truths must be perceived and appreciated. To such matured minds we say, 
read our book carefully, and speak your minds freely respecting its merits. 
For we believe, that the philosophic seeker for truth, of the present and future 
ages, will find in it sufficient immutable and valuable truth to approve and 
justify the time and labor spent by the author in his attempt to correct errors 
and to open the gates of scientific truth to mankind. The Author. 

Ecreka. California, January 25. 1879. 



TXT ROD TJCTION. 



w Philosophy and the intellectual sciences like statues," says llacon, u are 
adorned and celebrated, but are not made to advance; nay, they are frequently 
vigorous in the hands of their author, and thenceforward degenerate." This 
remark of Bacon's is litterally true of Lo*ic; which word will probably 
suggest to the reader that class of studies at the present time more nearly 
related than any other to the subject-matter of this book. And in attempting 
to explain something new and unknown to the reader, we are frequently 
obliged to make ourselves understood by reference to something already 
known. In our introduction of the reader to the explanations and substance 
of the science which we have endeavored to exhibit in the subsequent Dages, 
therefore, we would ask and expect that he has some knowledge of the stand- 
ard works upon logic, among which that of Archbishc p Whately is as able a 
specimen of the received systems as any; and as it is condense and contains 
but little irrelevent matter, it is therefore to be preferred to any other. We 
do not, however, insist that the following pages can not be understood with- 
out such previous acquaintance with the works of others. We have endeav- 
ored to make this treatise as elementary as possible; so that it may ! e in 
itself sufficient to convince and instruct the reader in its various doctrines- 
Yet such previous acquaintance with the popular works on logic will have 
brought any one to some appreciation of some of the difficulties in the way, 
and therefore he will be better prepared for the investigation. And we do 
positively insist that the reader shall come to the consideration of this book 
with a trained mind. 

On the other hand we do not object to the popular systems of logic 
because that science has not in the succeeding ages from Aristotle, its author, 
unraveled itself into greater number of details, or varied its elementary prin- 
ciples. True principles are immutable, and to depart from them is to fall into 
error. But the popular systems of logic, in our estimation, possess no value 
except in disputations; they are in fact what Archbishop Whately says of 
logic in general, l E thvly conversant about language." That the pop libit 
systems of logic make the analysis, and explain the true processes of the 
mind in reasoning, we do not believe, and therefore we do not regard them as 
of any value in assisting any person in his search after truth. In driving 
men by their own words to admit what thev already know to be true, i. e., in 
argumentation, they may be of value; but in making inferences from truths 



known to truths unknown, the mind does not proceed upon the principles 
set forth in the Aristotelian methods, and therefore these methods are of no 
value to science. In the language of Bacon "They force assent not things." 
Although the dialects of Aristotle have been before the world for many cen- 
turies, yet no one, however well acquainted with the system, has advanced to 
one new truth in science by the method therein laid down. And if logic is 
not a peculiar method of reasoning, but the method upon which all true 
reasoning proceeds, as contended by .Whaley and others, then the great 
advance which has been made in the sciences must have been made without 
reasoning at all, or else the method of reasoning is not such as it has been 
stated and explained by those authors. 

But although the popular systems of logic are of no value in assisting 
to lay the foundations, or to rear the superstructure of the physical, abstract 
or mental' sciences, yet for the purposes of adorning and giving force to speech 
they are not without value. Archbishop Whately regards rhetoric as the off- 
shoot from logic; in our estimation all that is valuable in the popular systems 
of logic belongs more properly to rhetoric than to any other science. It is 
true that whenever we reason i.e. we make inferences from truths known to truths 
unknown, certain processes take place in the mind, and that these processes 
are alike in the minds of all men who reason correctly. It is also true, that 
the popular systems of logic explain with tolerable correctness the manner of 
wording our premises and conclusions in what is called ratiocination. And 
to go even thus far is an acquisition of no small value. But it is somewhat 
strange that writers on logic, of the most brilliant talents, who so frequently 
warn us against the liability of being imposed upon by w >rds, should yet 
never have penetrated beneath the words to the things that have brought 
about these words with their manner of usage. Words are used in every 
science; but no science constructed upon word3 can touch the limits of things 
in mental or physical nature. The processes of the mind in reasoning leave 
no sensible trace behind them ; words do not stand as sensible signs of these 
processes. The mind b) its processes forms words, but the processes them- 
selves are at the bottom, and they lie deeper than the words. " A proposi- 
tion," says Whately, " is defined logically a sentence indicative i. e. affirming 
or denying; (this excludes commands and questions) sentence being the 
genus and indicative the difference, this definition expresses the whole 
essence; and it relates entirely to the words of a proposition." Any one can 
easily see that the above definition is grounded entirely upon grammatical 
distinctions, and as stated by Whately, "It relates entirely to the words of a 
proposition." 

To make a scientific analysis and explain the processes of the mind in 
reasoning require a different, treatment and mode of investigation from that 
hitherto pursued by writers upon l)gic. And we may in truth say that- in the 



pages of tins book, we have pursued a method, in the greater part, unaliena- 
ted heretofore. And certainly the exigencies of the world demand a better 
philosophy of reasoning than writers heretofore have given If we look 
about us in our own country, or travel abroad and observe the various onin 
ions concerning the most common affairs and effects, and notice the zeal with 
which men pursue the most absurd theor.es, we will conclude with the erelt 
English philosopher, that "the specious meditations, speculations and theories 
of mankind, are but a kind of insanity, only there is no one to stand by IS 
observe it." It is true that madmen may agree pretty well on many poinU 
and the grave digger in the play thought that Hamlet's madness woufd Vol 
be noticed in England among a people as mad as himself. And notwithstanT 
ing the advancement which has been made in the arts, and many of * e 
sciences during the present century, men yet are driven about in their od n 
ions as though there was no certain truth to be obtained, or else they pur ue 
some absurdity as though error and truth both were in effect the same th Dff 
And from these sources ot trouble, which set men to travel the wrong- road 
to happiness and true progress, there is no escape for mankind except In the 
further development of the sciences. But in the words of Bacon "The ores 
ent systems of logic are useless for the discovery of the sciences," and •?£ 
rather assist in confirming and rendering inveterate the errors founded on 
vulgarnotions than in searching after truth." 'ounaeci on 

"The unassisted hand," however, "and the understanding left to itself 
posers but me power Effects are produced by the means of ins.r^m enll 
and helps, which the understanding requires no less than the hand " And £ 
looking after helps for the understanding, we would naturally inquire bv 
wha means any one, who had made discoveries in science, had been assisted 
in his efforts. If any one should see a mathematician calculate th e Zs Tee 
to a certain object, or tell the night of a tree without measuring it and h ' 
find the result to be'as the mathematician had stated, he would very natural! v 
inquire how such knowledge could be obtained; by what means could uch 
conclusions be reached. And every one knows that the science of mathe 
ma ms is a most powerful instrument for solving those problems of „a ture 
winch come within its province. But the science of mathematic itself h as 
been discovered and ns truths have been brought to light by certain processe 
of the ,nd And those processes of the mind, whieh have broughfto TZ 
some truths in any given case, will, if exercised again in-like manner hrfnl 
to light other truths of a like nature. The miml ceKa nly possesses the 
power to gain knowledge by some method, and were this me,LTc ertai l 
known and clearly explained, it could be used to advance our knowTed ' u 
science unless all the subjects to which it is applicable are exhausted But 
he greater number of the sciences are confessedly yet in their infancy and 
the progress, which is made in them, seems to proceed in most in fauces 



rather by 'chance than by any direction which philosophers have <riven. The 
school -boy at the present day studies his logic; but the man who goes, forth 
in the search oi -truth, throws it away expecting no help from it. Those 
men, who have advanced science the most, have paid but little regard to 
those philosophers who have treated of the science of reasoning-, while those 
who have looked and relied upon help and direction from such philosophers, 
have produced nothing of importance. No person, who has made discoveries 
in science, will, upon reviewing his experience, acknowledge either that his 
mind had been led to use habitually the mode of reasoning always to be 
adopted, or that this mode was suggested to him in given cases by his previous 
studies of the iheoretriea! systems of reasoning used in the schools. Most 
persons, indeed, who have advanced science, have been so intent upon their 
conclusions that, they have not considered the processes of their mind* used 
in gaining those conclusions to be 'worthy of consideration. 

Rut if the true processes of reasoning were understood, reasoners would 
certainly be guided to advantage by such knowledge, and they would use this 
knowledge as an instrument to assist, their understanding in solving prob- 
lems in particular sciences. To assert that there is a science of reasoning and 
vet to say that this science is of no utility in advancing those sciences, which 
are built up by reasoning, is absurd. Ail irum admit that the greater part of 
ourknowledge is gained by reasoning, and reasoning certainly does not pro- 
ceed by chance — but upon some determinate process; and unless these* be 
legitimately pursued our inferences will be fallacies. 

JNTow the science of reasoning ought to inform us when we are in pursuit 
of any truth, which can be gained by reasoning, what method we must pur- 
sue in order to gain that truth: and if the s\ llogism as explained by the 
writers upon logic be the method of all true reasoning, then we must find a 
major and minor premises which will lead us to the truth in question-. But 
according to all the authors upon 'logic, when We lay (lownpnr major pi emise 
we virtually assert the conclusion; and hence we must* virtually gain the 
knowledge o( the desired truth before we can lay down the premises which 
shall conduct m to it, VYe repeat, however, Unit the popular systems of logic, 
are not only, not scientific works in themselves, but that they are of no use to 
science. And hence if we expect to lay sure foundations upon which every 
science can be built in ail their beauties of symetry, we must look after a 
better understanding of the reasoning processes than writers upon logic have 
been able to cxhib t hitherto. This we will attempt to do in this book. And 

we> are aware that tic task is not only in itself a wry difficult one, b:.t that 
the prejudices of scholars are against us. .Bacon's attempt to introdu e the 

inductive system of philosophy has cleared away in some measure the preju- 
dices of many in favor of \hi Arist >te!e 1:1 nvihoh. But B.icoa did not per- 
fect the indaeiive syst* m, and although he hi<- left here and there very 



9 

valuable hints on the other processes of the mind, yet he did npt systematize 
them, arid of the true principles of ratiocination he appears to have had no 
"better conceptions than Aristottle and his followers. For the most part, 
therefore, readers who have formed any bpinion upon such .matters, will, 
besides the difficulties of that subject, have to overcome prejudices in their 
study of this book. A careful study we believe, however, will conquer thos3 
prejudices. 

Before proceeding to the details of a treatise it is usual with writers to 
give some definition of the science which they claim to teach in their work,, 
and we will probably be expected to do the same. Some writers have defined 
Logic to be the art of thinking; others call it the science and also the art of 
reasoning; and still others consider it to be the science of the laws of thought 
as thought. For ourselves we do not expect that any definition of Algebra, 
which can be framed, will assist the student of that science very much in his 
studies, and therefore, a definition of that or of this science at the outset we 
do not consider of importance. But besides this we do not wish by a defini- 
tion to put a band around the inquirers thouglfts in the beginning. If a 
definition convey wrong impressions, it must fetter the mind in its contempla- 
tions ; and to lead a reader who has not yet studied the science, by a defini- 
tion to understand the whole drift of the matter would require a full exposi- 
tion of the definition,^, e. a full treatise upon the definition. We may say, 
however, that tmS present treatise is a scientific work, and that the science, 
whose principles are herein set forth, differs from all other sciences in the 
respect that it shows the only keys which can be used in unlocking the 
mysteries of any science. And hence, in general language, this work may be 
called the philosophy of science. In the title page we have denominated it 
the Organon of Science — not either from honor or derision of Aristottle's 
Organon ; but because in it we propose to show the instrument or instruments 
by which sciences are constructed. Bacon called his w®rk the "Novum 
Organ um," and since his time several works bearing that name have appeared, 
all of which, so far as we know, follow Aristottle rather than Bacon. 

The word logic has so many vague meanings in the minds of men at 
the present day that we have used that word but little in this treatise ; although 
our aim and the aim of most writers upon logic are so far the same that they 
both propose to lay down some method by which we may be guided and 
kept from errors. We, however, go much further and assert that our method 
exhibits the mental foundations of all the sciences and the modes of their 
construction; and that by the judicious application of our method, whether 
tfhe thinkers were or shall be conscious of it or not, discoveries in any science 
alwa} r s have been made, and always must be made, it made at all. Nor do 
we believe that we are endeavoring to excite vain hopes when we say that, 
the thorough. understanding of this treatise by the scientific men of the world 



10 

can not fail to open to the world a more prosperous era for science than it 
has had hitherto. And therefore we have the boldness to call upon scientific 
men and upon all meo, who wish for the prosperity and advancement of the 
human race, to give their serious attention to it, so that intelligence may work 
out order and happiaess in our civilization. 



book: t. 



CHAPTER I. 
Highest Generalization and First Division. 

In every endeavor to prosecute science, we start by dividing off and 
classifying those entities, which are familiar to us, and which are to be the 
subjects of our consideration. One class of philosophers, for the purposes 
which they have in yjew, divide the objects of earth into the animal, vegetable 
and mineral kingdoms • and under each of. these cjasses they make numerous 
subclassifications. The natural philosopher, technically so called, whose 
object is to ascertain the effects of material masses upon each other, the laws 
which govern them, and the changes which tlfey undergo without affecting 
their internal constitutions, commences by classifying matter into solids, 
fluids and gasses. The astronomer, the chemist, the philologist and historian, 
have each of them their subjects, objects and classifications. And the 
necessity of a proper classification, in order to reduce any subject to a science, 
will readily be perceived from the following consideration : Suppose a cer- 
tain field to contain several specimens of each of the classes of animals and 
a eertain person to enter it for the purpose of acquiring knowledge, if his 
mind should not generalize and classify, though he might multiply observa- 
tions for half a life time he must leave the field eventually without having 
gained any scientific knowledge. In order to succeed, therefore, th« naturalist 
commences to classify; and his field of observation being animate nature, he 
seeks for the highest generalization, which his mind . can make, and which 
may embrace in one class, all the objects of his regard. Bach subject beforo 
him, he perceives, has something in common with every other one, to-wit, 
animation : and to this highest generalization, he gives the name of animal 
to distinguish his whole field of research from other things. He then seeks 



12 
tor other less extensive generalizations, and soon perceives vertebrata, articu- 
lata, radiata and molusca. Thus the naturalist proceeds, and by classification 
alone, he is able to gain a scientific knowledge of the relations existing 
among animals. In like manner a proper classification of those things about 
which the laws of mind are concerned in reasoning, is indispensable to the 
clear understanding of the process employed in acquiring knowledge by reason 
ing: without a classification as a basis, all before us will be chaos. 

But how shall the metaphysician and logician classify? The object, at 
which he must aim, is*to obtain the knowledge of the relations, or rather the 
knowledge of the results of relations actually existing between -the mind 
itself and all other things, which can be made by the mind the subjects of its 
cognitions. ISTow every subject of the mind's cognitions must bear some 
relation to the mind itself or no result whatever could be produced. And in 
order to contradistinguish the objects between which the relations ^xist, from 
which intellectual results are evolved, the mind itself may be called tlVe ego 
and all other things the non-ego. The word non-ego, however, in this case 
is not a negative term in meaning, but a ptsitive name for any and everything 
excepting the ego, ©r mind itself. The German metaphsicians distinguish the 
mind itself by "Das Ich," and the French by "Le moi"; and Sir Wm. 
Hamilton has brought the ego and nOn-egp into vogue in the English nom- 
enclature. Most persons will know that ego is the Latin personal pronoun 
corresponding to our personal pronoun I of the first pe*«on ; ego is more con- 
venient to be used as a noun than our pronoun I, a single lettu* of the alphabet 
and therefore it is used. And we consider these contradistinguishing terms 
to be apt and useful ; for, between the ego and the non-ego, we are to look for 
the relations and results in question. But yet, how shall we classify the objects 
of our cognitions in a manner which will evolve and clearly set before us these 
relations and their results. We cannot clearly set before us these relations by 
a classification of the various objects comprehended in the non-ego, according 
to some peculiarities existing inter se, for this does hot in a sufficiently appar- 
ent manner, involve the ego* and unless both the eg i and non-ego be involved 
there can be no relations existing between them, and no results can be produced. * 
The classification necessary, as a basis of reasoning, must, doubtless, start with 
the highest generalization; for to plunge 'in medias res,' and classify certain 
objects, as plantigrade, and others as degitigrade, only points out the com- 
parative anatomy and relations of these objects inter se; and to classify the 
faculties of the mind into memory, will, imagination, etc., only brings out the 
relations existing between these faculties. The mind itself, or ego, is not in- 
volved in the^classlfication ; and consequently the results, springing from the 
relations of all other things to the mind itself, with their connections on the 
one hand with the ego, and on the other with the non-ego, can not be appre- 
ciated without finding a generalization, which shall comprehend them all. 



ft 

We must, therefore, seek the highest generalization of both the ego and non- 
ego that can be made, and taking this for our starting point, descend, divide 
and classify, in a manner very similar to that pursued by the naturalist. 

Now the highest generalization that our mind can make of both the 
ego and non-ego is existence. Existence is a term that may with propriety 
be applied to any and everything of which we can have any knowledge; 
each and every shade of thought and feeling, the active principle itself or 
ego; matter, space, time and the Deity, may each of them, be called an exist- 
ence; that which can be, and is, is an existence: and this is the highest 
generalization which we 1 can make of things; it includes the ego and all of 
the non-ego, the mind itself and everything else, of which we can have cogni- 
tions. Now the results about which we are concerned for logical purposes, are 
evolved from the relations between one existence, our mind itself, and all ©ther 
existences. The first division, therefore, of existences, in order to keep the re- 
lations^ the mind to other things in view, must be into the ego and nen-ego ; 
these are the two classes of things from whose relations our intellectual results 
are produced. The highest generalization itself of all things jitbout which we 
can have any knowledge, can not, indeed, be properly considered a class of 
things ; for, the term existence does not distinguish things inter se, but it 
merely distinguishes, as it were, things from no things, and sets up a state of 
being. But the classification of things into the ego and non-ego certainly 
puts before our mind, and exhibits to us distinctly the mind of the thinker him- 
self, and all other things which can be the subjects of the thinker's cognitions. 
And in order to make this classification more clear, we may consider it a 
little further. We, all o( us, believe there are such existences as trees, rocks, 
water and air, in short, that there is such a thing as matter ; we have gained 
a knowledge of such things in some manner ; and we believe that these 
things are not our mind, but that they exist outside of it, and are what we 
denominate the non-ego. Ws believe, also, that there are such things as 
notions, thoughts, conceptions, feelings, motiuns, etc., and although these are 
intimately connected with the ego, and could not exist without it, yet they 
are not the mind itself, but they are of the'non-ego. There is a wide differ- 
ence between the thoughts, feeling etc., produced, and the active principle, 
let it be wha^it may, which is engaged, in sonje manner in their production. 
Many of the thoughts of Shakespeare can be found in a book: the active 
principle, his mind itself, can not be found on paper; his works are the pro- 
ductions of his mind, not his mind itself. But again, we believe our own 
minds to exist, and that other men have minds. Now m^mind is to me the 
ego, but all other minds in reference to my mind belong to the non-ego; for 
every person must make his own mind alone the point from which and to 
which he must make all his bearings in gaining knowledge. But again we 
believe that there is space, time, eternity and that there is a God; and all 



14 

these things are non-ego.; my mind itself only for me and your mind only for 
you are the ego; all other things belong to the non-ego. 

Now for further classifications, we haye to deal only with the non ego: 
for the ego being, a single existence is incapable of division and subQlassifi- 
cation ; but the non-ego is capable of division ad infinitum, and therefore, 
we may nake numerous subclassifications of it. The non-ego, however, 
must always be subclassified with reference to the ego and not merely with 
reference to the constituents of the non-ego- inter se. The ego and non-ego 
merge in existence and this must be borne in mind; for, whatever relations, 
if any, may exist between the earth and the moon, t£ey never could be any- 
thing to us unless each of these objects sustain some relation or relations to 
the ego, my mind for me and your mind for you. That which bears no re- 
lation to the ego can not be the subject of our cognitions and it must be to us 
as though it had no existence; it is only by means of the relations of objects 
to our minds that we can gain any knowledge of the relations existing be- 
tween the objects themselves. In our classifications, therefore, it is impor - 
tant to keep in view and take the ego, my mind for me and your mind for 
you, as the point from which to run to every object of the non-ego. 

CHAPTER II. 
Pacts and Truths. 
Having in the previous chapter divided existences into two classes in 
such manner that the relations between ttoem will always involve the mind 
as one of the things related, we come now to the classification of the non- 
ego with reference to the ego. And a very obvious division of the non-ego 
with reference to the ego w@uld be into existences of the past, of the present 
and ot the future. Most of us, no doubt, have had friends whose phj sical- 
forms have passed away; their forms were existences in the past, out in the 
present they do not exist; and to-morrow is but a present thought concern- 
ng the future. But we must observe that, tlfese divisions only bring out 
the relations between points of time, in one of which points the ego is now 
situatBd; nevertheless, as the ego and non-ego are existences bearing towards 
each other the relations of time, these divisions, according to the points of 
time occupied by each, do bring to view the relations between the ego occu- 
pying the present point, and! those existences of the non-ego occupying 
the same and different points. But 'all the existences comprehended in 
the non-ego may be thrown into another classification, which shall involve 
the relations existing between the ego and non-ego in other respects than 
that of time and or that as well. 

The first sub-classification, therefore, of the existences ot the non -ego, 
which we will make, will be into pacts and truths. And in order that we 
may understand this division, it is necessary to consider the relations of the 






15 

ego merely as an existence among other existences. That which has had a 
beginning, must have been brought into existence by some anterior existence 
or existences. We will not stop to argue this point now, for we do not think 
it will be doubted. And if our minds have not always existed, their very 
beginnings of existence must be dependencies; and dependent existences 
come and remain as existences by the influence of that upon which they 
depend. And when other existences like itself with respect to dependence, 
surround the ego, the ego and these other existences must be so related to 
each other that they may act and re act upon each other, if each be affected 
by the other: and each is either affected by the other directly or indirectly,, 
or the one only is effected by the other, or neither the one nor the other is 
aftected by the circumstance of their both being existences. Now between 
material objects, it is declared to be a universal law of nature, that action 
and re-action are always equal and in opposite directions. Whether this law 
be extended to the relations between mind and mind, and between mind and 
matter, it is not necessary now fo# us to inquire. But of one thing we must 
feel assured, that the external non-ego, when its existence is the immediate 
subject of our cognitions, acts directly or indirectly on the ego. For a tree 
either acts upon and affects the mind, or to change the expression, the mind 
is affected by it in some manner, or the mind can have no cognitions of the 
existence of a tree, and it would be to the mind as though it were not. The 
mind had a beginning and therefore it is a dependent existence; and an 
existence, whose coming to be an ezistence is dependent, must ab initio be 
passive : and ils activity and pasivity both, must have been either given»to it 
simultaneously, or the former must have been developed from the later. For, 
the acting power of a dependent existence can not exist of itself independent 
of other things, but another or other existences are presupposed to generate 
it. And if the ego be dependent, its dependence must be upon the external 
non-ego, .otherwise it Would be independent; and dependence implies the 
reception of action. The dependent mind, therefore, independent for its 
existence upon the action of that part of the non-ego, from w r hich its exis- 
tence came, and for its knowledge upon the action oi that part of the ex^rnal 
n©n-ego, of whose existence it gains knowledge. 

Now at the first with respect to knowledge, other existences act upon 
the mind without its inherent energy being exerted. That we are boin with- 
out any knowledge, will not be doubted by any well informed student since 
the days of Locke. The mind must exist for a certain period in its inception 
without consciousness: for to be conscious at all, it must be Conscious of 
something : to be conscious of nothing is to be without consciousness : if 
consciousness can be contained in mere pasivity then a rock can be conscious. 
But activity is necesssary*to consciousness: and mental activity must be de- 
veloped from the mind's passivity by the action of that part of the non-ego, 



16 

upon which the mind's dependence in this respect consists. For the power to re- 
ceive an action must "be contemporaneous with the mind's existence: but the 
mind must exist in the w r orld before it can be acted upon.by any power, other 
than that which created its being before it w T as really a mind. When, therefore, 
the ego first comes into the relations of that part of the non-ego, from which 
its existence was not derived, it must first be acted upon aiad act in response 
before it can be conscious of that part of the non-ego. And when we reflec 
that the external non-ego affects the mind only through the senses, and that 
in the foetal state, all these senses, even that of touch in a great measure at 
least, are secured against external impressions, w T e can not doubt that the 
mind at first is unconscious of an external worhj. And the only other things 
©f which it could be conscious, are the action or actions of the power w,hieh 
caused it to exist, aod of its own existence. Now the action of that existence 
or of those existences which created the mind, must still continue to be 
exerted, or the ego becomes either an* independent existence or a non-entity. 
But we have shown the mind t© be dependent, if it had a beginning; and 
therefore we may with mature faculties appeal to our consciousness respect- 
ing the action of that creating power, and all persons will say that they are 
entirely unconscious of the action of that power which prolongs our existence. 
It is, however, commonly said that we are conscious of our own- existence, 
i. e., that the ego is conscious of itself per se; but we regard this as an error. 
For unless the mind act, it can not be conscious at all : and when it does act, 
it is conscious of Its acts, states and. feelings; but of itself per se it is not con- 
scious. Each person can test the truth of this by his own consciousness. 
And if the mind at first be unconscious of the action of the external world 
through the senses, and also unconsciousness of the powers which prolong 
our existence and unconsciousness too of its own existence per se, it must at 
first be without consciousness. The mind, indeed, can be conscious of its 
own acts and feelings ; but independently of the action of other existences 
upon it, it can not begin to act or to feel. 

Now we find that a material body made up of bones, muscjes, cartilage, 
men?branes, nerves etc., all of which belong to to the non-ego, contains the 
mind. This body is related both to other existences without and to the mind 
within: it is a medium between the mind and existences external to itself 
*And the first effect produced upon the ego by or through this body gives the 
mind merely that state of activity which we call intensified pasiyity. The 
mind does %ot yet notice; but it possesses more than mere passivity: it does 
not yet put forth its energy in any definite direction/but it possesses energy. 
But in a little time after birth, by being continually acted upon by the exter- 
nal world through the senses, the- mind's intensification is increased, and its 
energies start in definite directions, and then it notices. But it merely notices. 
By the eye, the ear and the other senses, It notices existences: but the where, 






1? 

the when, the what, or the why, it does not know. But in a little more 
time, the mind begins to discriminate and then it begins to know and to have 
knowledge. 

Without the power to discriminate, we <could know nothing, although 
we might notice some things : and the possibility of discriminating lies in 
the relations between the non-ego and the ego. Now the only relations, 
which can exist with reference to the ego, between the existences among 
which the ego is placed* and with which the ego itself must be contemplated 
are those between the ego and external non-ego directly, those between one 
external object and an other of the non-ego indirectly through the ego, those 
between one external and one internal object of the non-ego through the 
3go, and those between one internal object and another of the non-ego. 
From each of these relations and from them only can we discriminate and 
gain knowledge. - From the relations existing between the ego and the external 
non-ego directly, we have the action of the non-ego upon the ego, and the 
response of the mind itself in a directly opposite direction to the one received. 
This is the mere noticing of an object by the mind and it constitutes a fact. 
But if in the noticing of an external object of the non-ego, which is a fact, 
the mind also notices its own act, which, we think, is the case, here is another 
thing noticed, a fact different from the former, and these two facts may be 
compared. And let the same process be repeated with the same external 
object of the non-eg®, and we have a relation between two acts of the mind 
itself, between two internal objects of the non-ego; and also a relation be- 
tween each act of the mind and the external object. And hence among these 
relations, three cpmparisons may be made, viz., between each act of the mind 
and the external object, and between the two mental acts inter se: and from 
either of these comparisons, the mind can gain knowledge. From the com- 
parison between the action of an external object of the non-ego upon the 
ego and the act of the mind itself in return, we gain the knowledge, that the 
act of* the mind itself and the action of the external object are separate 
existences : and from the comparison between two aots of the mind itself, we 
can also discriminate and gain the knowledge of separate existences. For 
two acts of the mind in the same direction can not be simultaneous: and the 
interval of time, however small, forms a relation by which the mind can 
. discriminate and separate internal existences. Separate existences hereafter 
we will call heteka. (Greek— heteros, a, on— others). We use the neuter 
plural of the Greek adjective as a noun, meaning other things — separate 
existences. And hence the evolution of hetera by the mind is the inception 
of human knowledge^ By the mere noticing of an object, the mind indeed 
acts, but can know nothing, because one object per se can not be compared 
and discriminated. But if the mind notices its own acts in noticing external 
influences and compares them with that of the thing noticed, from the rela- 



18 
tion existing between the two, the mind can evolve the knowledge of hetera. 
And "we must here remark again, that the mind does not and can not notice 
itself. Its acts, states and feelings, it can notice : but the knowledge of its 
own existence, as a potential mind per se, is gained only by comparison. 

Now things merely noticed by the mind we call facts: the knowledge 
gained by the comparison of noticed existences, we call truth: and this is 
our first classification of the existences of the non-ego. Facts then, are 
existences, each ©ne of which is noticed by a singfle act of the mind and 
•without comparison: truths are the results of comparisons made by the 
mind between facts and also between truths themselves. Now pacts are all 
comprehended in the non-ego, and of them we may make two classes : the 
one class having their where without and- the other having their where 
within the ego. The first of these classes we will call perceptional and 
the second selfconsctonal facts. And although neither of these terms are 
in common use in, our language, we think we have the right to adapt 
terms to our own purposes. From the Latin fractio, we have Traction, from 
which the adjective fractional is constructed : and from perceptio, we have 
perception, from which in like manner perceptional may be made in har- 
mony with the principles of our language. And thus, also, we may deal 
with conscio and prefix self. 

And each of theses classes of facts may again be divided into five sub- 
classes. Perceptional facts are naturally subclassified into the five classes, 
viz. : visual and auricular facts, facts of touch, of taste and of scent. And 
hence one external aggregate existence— and by aggregate existence we 
mean an existence to which we can apply our organs of touch, of taste, of 
smell, of sight and hearing— may contain five perceptional facts or external 
noticeable existences. Such an existence as red, or an existence to which 
we can apply but one specific organ of sense, we call a simple existence and 
not an aggregate one. But two aggregate existences, then, will contain 
ten perceptional facts. And if each fact of the same aggregate existence, 
be compared with the others, there will be ten comparisons of facts inter se 
of the same aggregate existence. And if we compare each fact in an aggre- 
gate existence with each fact in another aggregate existence, we w 7 ill have 
twenty-five comparisons. And hence two aggregate existences contain ten 
facts and afford forty-five comparisons, from all of which truths can be gained. 

CHAPTER III. 

CONSCIOUS TRUTHS.. 

lb the preceeding chapter we explained what we mean by facts and 
endeavored to show to what existences we apply that term. We showed that 
those existences which w6 call .facts; in and by themselves separately con- 
sidered, make no part of our knowledge; but that they are the foundations 



19 ■ 

and pre-exislent substrata upon which all our knowledge stands and from 
which it springs. All knowledge lies in relations, and the mind evolves it 
by comparisons. Were a person so brought into life that he could .see the 
sun, i. e., notice this perceptional fact, but notice nothing else, i. e., have no 
selT consclonal fact, he could not know that the sun exists. We can not say 
that the sun exists without having the knowledge of existence. For, the 
phrase "The sun exists," or "The sun is," is equivalent to this, viz.: the sun 
is an existence. And unless we first have the knowledge of existence, we can 
not know the sun to be one: not a single fact but pacts must come to the 
mind before knowledge begins. And when the mind first notices a percep- 
tional fact, there is also always lodged in it a self-conscional one; these facts, 
the one perceptional and the other self-conscional alway enter the mind in a 
binary manner. For, as we have already said, the ego unconscious of itself 
per se, takes its place among other existences to be acted upon and to act in 
return. And these perceptional and self-conscional facts keep com ins: in a 
binary manner repeatedly before the mind compares them at all: but when it 
does once make the comparison, the knowledge of separate existence is 
evolved. This knowledge we call conscious truth. And hence we say that 
we are conscious of an existence though the knowledge of an existence be 
not a fact to us, but a truth evolved from the relation of facts : the fact of an 
existence per se is noticed but not known by us. 

The relation of perceptional and self-conscional facts is necessary to 
the beginning of consciousness. For, as already said, to be conscious implies 
to be conscious of something, and to be conscious of nothing is to be without 
consciousness; and the human mind had' a beginning of existence and it is a 
dependent being. And although, indeed, we can not tell by the proofs which 
nature offers, but that the materia mentis, so to speak, may haYe always 
existed, and that at the first it may have been inclosed within a human body 
and afterwards handed down from generation to generation ; yet that there 
was a time when our consciousness did not exist, is clear. For, the -materia 
mentis, let it be what it may, could not y per se, by its own inherent power 
separated and independent of all things else in the universe, be conscious of 
anything except itself per se. And although the mind be conscious of its 
acts, states and feelings, yet that it is not conscious of itself, i. e., not con- u 
scious of the fact of a materia mentis, our own consciousness teaches us. 
And if the mind be not conscious of ftie fact of its existence, or to use a 
phraseology more tangible to some minds, if the mind can not feel itself per 
se, it must be a dependent being, and its dependence must be a dependence 
in every respect at least except existence alone. And that the materia mentis 
in such relations as entitle it to be called a human mind had a beginning can 
not be denied : and hence its conciousness in those relations must have had a 
beginning also. And as the human mind is inclosed within a body, were 



20 
this body impervious to the action of all external things, the mind must con- 
tinue unconscious. And although it is often said that consciousness is the 
very thing that distinguishes animate life: yet the lack of actual conscious- 
ness does not establish the lack of potential consciousness or the nonentity 
of mind. Consciousness is not the mind itself: the materia mentis must 
first exist before consciousness can. And if, as we have shown, the mind in 
order to be conscious, must be conscious of something, that something of 
which it is conscious, must be brought to the mind itself by the external 
non-ego : otherwise the human mind could rear a structure of know4edge 
from out of itself aad independently of all things else'in the universe. Con- 
sciousness, therefore, as it can not exist without a minci to contain it, so like- 
wise it can not exist in the human mind independent of all things except the 
mind: without the non-ego the.eg&.could not be conscious. 

Now there is in man a meteria mentis, or an immaterial substance, or 
it you please and as some suppose an arrangement of physical organs in some 
manner go that the arrangement aftords the conditions necessaryn to become 
conscious when. acted upon: we start no question respecting either of those 
or of any theories. What may be the essence of mind, we do not know, but 
whatever it may be, we find it, in a. proper organization, to be capable of 
knowledge; and our inquiry here is- with reference to this knowledge. And 
the first knowledge, which the mind gains, is conscious truth. And if 
consciousness depend upon the relations of facts, L e., upon existences which 
are inter se hetera, it must spring from those relations. We may say, that 
the mind has knowledge of something. This sentence contains the*mention 
of three existences viz. : mind, knowledge -and thing. We may say that the 
mind is conscious ot something; and this sentence contains mind, eoncious- 
ness and thing. And if, as we have shown, the mind notices its acts, but not 
itself, and consciousness be dependent for its existence, then, if the later sen- 
tence be true, consciousness must have been evolved from the relation of the 
action.ot the 14JND, and that of the thing. An object of the non-ego affects 
the materia mentis, the mind acts; and from the relation of the effect pro- 
duced upon the materia mentis, and the returned action of the inind, spring 
consciousness or the knowledge of existence. Consciousness is the result of 
relations and it*js envolved from facts. When we say that we know that 
stove is not an act of our minds, because we are conscious of this, we state 
what is not true. We become conscious of the existence of an act of mind 
and of a stove, and the judgment then discriminates between the two by 
comparison. Conciousness is merely the knowledge of existence; and the 
thing or existence of which we are conscious, we call a conscious truth. 

Now we have shown that there are perceptional and ,self-conscional 
facts; there will be evolved therefore, from the relations of these tw6 classes, 
conscious truths grounded in the non-ego and also conscious truths grounded 



21 
in the ego. And as numerous as the perceptional and self-conscional facts 
may be, so numerous will be the conscious truths. For every relation be- 
tween perceptional and self-conscional facts evolves two consctonal truths. 
The relation between the perceptional fact of a tree and the 'self-conscional 
fact of the mind's act in noticing that tree evolves two conscious truths, the 
one being external and the other internal. From the relations of self-con- 
scional facts inter se, however, or from the relation of perceptional fac:s 
inter- se, conscious truths can not spring. From the relations of perceptional 
and self-conscional facts, spring conscious truths, and then these conscious 
truths can be compared promiscuous!}'. Conscious truths, therefore, like 
perceptional and self-conscienal facts, upon which they immediately depend, 
come to the mind in a binary manner. 

Now by each of the five senses, the mind notices perceptional facts: 
when these facts by their relation to self-conscional ones, rise into conscious- 
ness, they become conscious truths which are grounded in the non-ego. So 
likewise when self-conscional facts from their relation to perceptional ones 
rise into consciousness, they" become conscious truths, which are grounded in 
t lie ego. There are, then, two great classes of conscious truths, viz: con- 
scious truths grounded in the non-ego, and conscious truths grounded in the 
ego. But that the one class is grounded in the ego and the other in the non- 
ego, is not determined by consciousness, i. e., we are not conscious of that, 
but this knowledge arises from an act of judgment in comparing two con- 
scious truths, i. e., tw T o "existences ef which which we have become conscious. 

How it is said by some philosophers, that the mind does not occupy 
space, i. e., that space is not necessary, not one of the. conditions of its 
existence. But nothing certainly can be more absurd: for that, which does 
not exist anywhere, can have to existence. Because we can not {ell the 
precise where, in which it does exist, does not prove that-it has not a where 
in /which to exist. That, which has an existence now t here, has no existence 
at all: and eveiy where is a where in space. ^The ego exists somewhere 
and in this viieee lie the conscious truths grounded in the ego: the non- 
ego exists somewhere and in this where lie the conscious truths grounded in 
the non-ego: the wheres of the ego and of the external non-ego are hetera 
of space. Now r we must recollect that the conscious truths grounded in the 
ego and those grounded in the non-ego come into existence simultaneously; 
the only things therefore, wkich the mind can discriminate, between con- 
scious truths grounded in the ego and conscious truths grounded in the non- 
ego, merely as existences, are the wheres occupied by each, i. e., the wheres 
can be discriminated into hetera. We pl^srify, therefore, all conscious truths 
into conscious truths grouncled.in the ego, and conscious truths grounded in 
the non-ego: and that these two classes of truths respectively are thus 
grounded, the mind determines by heterating their wheres. Each of these 



2% 
great classes of conscious truths may be again subclassified; The conscious 
truths grounded in the external non-ego are classified into conscious truths 
of touch, of taste, of color, of scent and of sound; and the conscious truths 
grounded in the ego y into hearing, seeing, feeling, smelling and tasting. All 
these, both those grounded in the aon-ego, and those grounded in the ego, 
are inter se hetera. A sound is not the same thing as hearing, nor a scent the 
same as a sougct; any two of the same class or of different classes, are hetera. 
And hence of the conscious truths grounded in the non-ego there are five 
classes, and of the conscious truths grounded in the ego* there are five classes, 
making in all ten heterical subclasses of conscious truths. 

' * CHAPTER IV. 

NOMINAL AND PROPOSITI ON AL TRUTHS. 

In the last chapter we endeavored to show what we mean by conscious 
truths. AVe do not mean nvy conscious truths, truths which possess con- 
sciousness, but existences of whose entity we become conscious. And we 
showed that w r e gain the knowledge of conscious truths by being able to 
separate the external and internal existences of the non-ego into hetera. 
This is the first step in the acquisition of knowledge. And were we not 
able to do this, all would be chaos; but this once done, chaos breaks and 
order takes a beginning: and then we proceed further and discriminate in- 
ternal existences inter se, and also external existences inter se into hetera. 
But, as yet, we know heterical existences, we have the knowledge of existence 
merely as existence; and merely as existence, existences are all alike. A 
sound, a taste, a color, etc., merely as existences are hetera but alike; they 
are, as existences, heterical similia (Neuter plural of Latin ; similis, e — things 
resembling each 'other). 

But Sound, taste, scent, color and touch, being existences grounded in 
the external non-ego, may be further discriminated by the different modes or 
manners by which they are related to the ego. And hearing, seeing, smell- 
ing, tasting and feeling being existences grounded in the ego may also be 
discriminated inter se by the modes or manner by which they are related to 
the external non-ego. The manner of receiving visual impressions and see- 
ing is different from that of receiving aricular impressions and hearing. 
And this difference of mode or manner, whether there be any other differ- 
ence or not, distinguishes the five classes of conscious existences grounded 
the non-ego inter se, and also the five classes of conscious existences grounded 
in the ego inter se. These modes or manners by which the mind is brought 
into relations with the external non-ego, belong to onr physical organiza- 
tions, and inter se they are deferentia (Neuter plural of Latin differens, ens 
— things differing. 

By DiF^ERENTrA we do not mean difference, but things differing, hetera 



23 

unlike. Tire difference between two feet and one foot is one foot: the differ- 
ence in area between a parallelogram and triangle of the same base and 
altitude is one-half the area of the paralellogram : but the difference between 
red and green can not be pointed out. The difference lies in the causes of 
these effects upon the mind; but what those causes are, w r e do not under- 
stand sufficiently, so that w r e can contemplate them otherwise than by the 
effects themselves, which we can only discriminate into things differing — 
differentia, If we resolve a raj of light into its elements by the prismatic 
spectrum, and then from differeat combinations of elements, each combina- 
tion having one element at least in it the same as in the others, we find 
different colors to result, the difference between these combinations, is the 
additional element or elements in the one more than in another: but the 
difference between the effects per se of these combinations upon the mind, 
we can not point qut. That these effects per se are differentia, hetera unlike, 
we know ; but that is all we know about them per se. 

Now had it been possible for l^an to have become conscious of only 
one existence, he never would have invented a name for that existence. For 
everything which has a name, has leceived that name to distinguish the re- 
sult of a heteration of a differentiation or of a comparison of things. Suppose, 
for instance, that every object of vision had possessed but one color: no dis- 
tinguishing name then for any color to distinguish it from others, could have 
been introduced into language. For the word u color," would have expressed 
all the knowledge that man could have had in that regard. And although 
this existence (color) would have arisen into consciousness: yet the only 
necessity in a name for it, would have been to distinguish it from conscious 
truths of the other senses. And unless men became conscious of the very 
essence of existence they could by making; some possible discrimination 
give names only to distinguish existences inter se. And supposing now, all 
the senses excepting sight to be wanting, and all objects to vision to possess 
but one color, then there would be no other existences grounded in the non- 
ego to discriminate inter se, and the w T ords seeing and color would have 
been sufficient to discriminate the parts of man's knowledge. But suppose 
now that along with the one color, ojie existence of sound should rise into 
consciousness, here now is an existence of a different mode, possessing Ja 
different relation toward the ego from color. There is, indeed, no assignable 
difference within our knowledge between a color and a sound per se, they are 
simply differentia, hetera unlike; and their modes ot relation to the ego are 
differentia: but the difference between hearing and seeing per se cannot be 
pointed out. The differential modes of relation, gjve us the knowledge of 
the differentia, sound and color. And now, upon the above supposition, we 
know one sound and one color, and know these tw 7 o existences to be differ- 
entia : and to distinguish these two existences inter se by words, two namrs 



24 

are necessary. A name for the one existence alone, will not answer to enable 
us to mention the other. If we should call the one color, not color might 
stand for the sound. But suppose now ascent also to rise into conscious- 
ness: we have now three differentia: and if we wish to speak of them, we 
must have three distinguishing terms, one for each: and so on through the 
senses. 

And hence w T e see that there will be five generic names in every lan- 
guage, wiiich has attained to any perfection, to distinguish the five differentia 
of. conscious truths- grounded in the non-ego. These names are signs of the 
results of the mind's discriminations by modes of relation among conscious 
truths grounded in the non-ego. A like discrimination is also made with 
like results among conscious truths grounded in the ego. But in giving 
these names, men are not naming facts, nor are they naming conscious truths 
jier se; but they are giving names to distinguish conscious truths inter se. 
Facts grounded in the non-ego pei se, have "no names to distinguish, them 
inter se: conscious truths per se have but one common name, to-wit, exis- 
tence; but conscious truths, which are inter se differentia, have five names 
for those grounded in the non-esro, and five names for those grounded in the 
ego: each oi the differentia is in language distinguished from the others by 
a name. These truths spoken of, which are inter -se differentia, and grounded 
in the ego and in the non-ego, w t o will call nominal truths: because they 
are the first truths distinguished bv differential names. The nominal truths, 
then, are sound, taste, color, touch, scent and the hearing, seeing, feeling 
smelling and tasting: all these are inter se differentia. We do not mean, 
however, that these truths were historically the first truths named. The pro- 
genitors of our race would be likely to give names to aggregate existences 
first, as they would come in contact and fee.1 deeply interested in them from 
the beginning. But philosophically, when attempting to reduce our knowl- 
edge to scientific order, nominal truths come up next after conscious truths 
and they are the first truths distinguished by differential names. 

Now proceeding with our inquiry, as we have called differential con- 
scious truths, nominal truths; so the truths gained by differentiating nominal 
truths inter se, we will call primary prepositional, truths: because they are 
the flrit ones that can be exhibited in propositions in which the words no, 
none and not do not occur, and in which the subject and predicate are not 
represented by the same name, as tied is a coler. And for the present, we 
will dismiss from our consideration, those truths grounded in the ego, and 
consider those only, wiiich are grounded in the non-ego. Suppose all the 
existences ot vision presented to our eyes for twenty years of our life, to 
have had but one color, green for instance: and supposing all of the senses 
to exist in a healthy state, at the end of that period, we would have the nom- 
inal truth of color, and some name to distinguish it from the nominal truths 



25 
of the other senses: suppose this name to be color. And suppose that an- 
other existence, red for instance, should then become a conscious truth. 
Now if we should compare this new existence with all the others of which 
we had any knowledge, excepting green — the first color, we would perceive 
that it was not on the same scale of truths, like any of them in any respect. 
As a conscious truth it is like them all ; for all of them are conscious truths. 
But as a nominal truth, a further consideration and discrimination, this new 
existence has nothing in common with any of them. But if we compare 
this red with that green, we perceive that they both agree in their modes 
of relation to the ego ; and it was because the modes of relation to the ego 
are differentia that the conscious truths of sound, taste, scent, etc., could be 
discriminated into differentia — into nominal truths. But in the case of red 
and green, fche modes of relation to the ego are not differentia, but similia, 
aud hence red and green, as conscious truths, can not be discriminated at all 
into differential nominal truths; but we must proceed further and discrimi- 
nate inter se nominal truths (to which both red and green belong, and there- 
fore the word color is applicable to both), into primary proposilional truths. 
Red is discriminated from the conscious truths of the other senses, in the 
same manner that green is, and the name color may be applied to both and it 
sufficiently distinguishes them from the other nominal truths; but it does 
not distinguish red and green inter se. And to do this we must necessarily 
discriminate colors* This we are able to do. And the reason that we are 
able to discriminate colors, lies not in their modes of relation to the ego, bujt 
in causes, which are differentia working through modes, ^vhich are similia: 
the modes of relation to the ego are similia, but the relations themselves are 
differentia: and to distinguish these relations inter se two names must be 
used. Red and green, therefore, as nominal truths, are both distinguished in 
language by the name color; as primary propositional truths, the one is dis- 
tinguished by the name red and the other by green. And hence w T e can 
say that this color, this nominal truth distinguished by its mode, is among 
truths of the same mode, distinguished by the name red: this color is red. 
And if we add another color to our list, we must deal with it in like manner, 
and similate it with the nominal truths of color, and then differentiate these 
similated nominal tritfhs into primary propositional truths ; and so on through 
the colors. And if we now call color a genus, as is generaHy done by 
logicians, we will then have species of color. And thus we may deal with 
scents, sounds, tastes and feelings. 

And hence we see that primary propositional truths arise by comparing, 
and generically similating and specifically differentiating nominal truths. 
And these primary propositional truths, which as primary propositional 
truths agree in every respect, will of course, be classed together, i. e., will 
have a common name for each and every one of the individuals thus alike: 



2$ 
just as all nominal '.truths inter se similia, will, as nominal truths, have a 
common name. Take the primary propositional truth red, and suppose two 
lieterical reds to be before us: now two heterical reds as primary proposi- 
tional truths, are exactly alike in every respect, starting from the facts, 
which lie at the foundations of them. They are both perceptional facts: 
both are conscious truths grounded in the non-ego, both are nominal truths, 
and both are primary propositional truths: but we' can carry our discrimin- 
ation no further. As primary propositional truths, !hey are alike in every 
respect in every step from facts: and could, we not at the second step, exist- 
ences grounded in the non-ego, discriminate them into hetera, they would 
be to us the same tiling. And in this manner are sounds, colors, tastes, scents 
and touches divided and classified. 

The nominal truths of sound are divided into musical and non-musical. 
And the primary propositional truths of musical sound are again divided 
into rythmics, melodies and dynamics: these last are secondary propositional 
truths. Non-musical sounds too are frequently subclassifled by calling to 
our mind and connecting with them some object which is supposed to pro- 
duce them, or some state or feeling of the mind itselt, which certain objects 
produce; as vocal, nasal, pleasant, dism.il, deathly sounds, and so on. But 
there are, no doubt, thousands of truths perceived by the mind without names 
to distinguish them. For the colors, which are differentia, and the sounds 
which are differentia and so on, are very numerous, and only the very appre- 
ciable and marked ditierentia receive distinguishing names. Now conscious 
truths, nominal truths, primary and. secondary propositional truths, exhaust 
our knowledge of ttoose simple existences, which we will have occasion 
hereafter to call facial gregaria. 

CHAPTER V. 

ORDINAL, CARDINAL AND TEMPORAL TRUTHS, AND TIME AND SPACE. 

Having in the hist chapter treated of those existences, which we will 
have occasion to use again in" our inquiries under the name of facial gregaria, 
we must now proeeed to classify still other truths, which enter into our daily 
concerns of life, and from which we continually reason. We have already 
shown hetera to lie at the very foundation of our knowledge. And although 
the unit is the first of the series of cardinal numbers and the base of the 
system, yet duality or plurality is necessary to our knowledge of the unit. 
Without the knowledge of two existences at least, we could not have the 
knowledge of the unit. For, the knowledge of one springs from numerical 
relations; and with one existence per se there can be no numerical relations. 
Now we have already seen that, differentia receive distinguishing names. 
But hetera also receive names to distinguish them inter se. If we compare 
one conscious truth with another, and cannot discriminate them into nominal 



27 
truths, i. e., into differentia, the only way that is left for us to distinguish 
them ai all by names, is to mark them first, second, third, etc., and this result 
is accomplished by distinguishing existences merely into hetera and marking 
the individuals. These truths, therefore, we call ordinal truths. They 
come to our minds in point of time at an early period of our knowledge: but 
they may not receive names to set them out clearly for' a long time after- 
wards. Ordinal truths are simply the relations of separate existences as ex- 
istences and their names distinguish the individuals inter se. And hence 
these names may be applied to anything, just as we may call anything of 
which we have knowledge, an existence. And in point of time the ordinal 
truths or numbers, philosophically considered, must come to our minds be- 
fore the cardinal truths or numbers. And historically, this appears to have 
been the case. We find the ancient Jews, Greeks and Romans, using for their 
notation the first ten letters of the alphabet, which upon reflection will be 
seen to express much better the ordinal than the cardinal numbers, and for 
which purpose they w T ere most probably used at the first, and for which they 
are now with us exclusively used. 

And after the ordinal numbers or truths are obtained, we have but to com- 
pound or colligate them and name the colligations (for in nature they will 
be sim-ilia hetera unlike) and we will then have the cardinal truths or num- 
bers, Cardinal truths, therefore, are collegations of hetera with a defer- 
ence inter se of one, and they are distinguished in language by the names 
one, two, three, etc. And as each colligation is a colligation merely of hetera, 
the distinguishing name given to any colligation may be given to a like 
colligation of things differing in nature^from the first, as two men, two 
horses, etc. The abstract nature and applicability of numbers to any and 
everything, is owing to the circumstance, that they are names of hetera, 
which do not take into consideration, in any manner, differentia in nature, 
but which merely represent heierical existences. When, however, we apply 
these numerical names to objects in the concrete, the objects must be heteri- 
cal similia. We can say that a potato and a horse are two existences, but 
we can not place after the word two any differential name by which we can 
express, in the concrete, the numerical sum of a horse and a potato. 

But again : we have already seen that facts, the one perceptional and the 
other self-conscional, enter the mind in a binary manner, and from their rela 
tions, acts of the mind itself become conscious truths, known existences. And 
conscious trutfis grounded in the ego may be compared inter se, and from 
their relation* another class of truths may be evolved. If two acts of the 
mind in the same mode and direction, be discriminated, we will have the 
temporal truths of once, twice, thrice, etc. Whether a man can hear, see, 
smell, etc., all at the same time, which is probable, we will not discuss. But 
that a man can not see or hear, i. e., that the mind cannot act in the same 



28 

mode and direction in either hearing or seeing twice at one and the same 
time i& evident. Place an object before you and look at it, and then after, 
having taken your eyes away from it, look at it again, and you will not say 
that you have looked at it twice at one and the same time. The comparison, 
therefore, of two conscious truths inter se similia, grounded in the ego 
evolves the temporal truths of once, twice etc. 

But again: if we resolve existences grounded in the non-ego into 
hetera, we will, of course, perceive a plurality of existences. And if the 
modes of relation to the ego, of two existences so resolved at the same time, 
be the same, we must perceive that the two existences do not occupy the same 
where, for if they did we could not, at the same time, resolve them into 
hetera. Red* for instance, which occupies but one point, can not at the same 
time be resolved into hetera, into separate existences, into two reds. Heter- 
tcal existences grounded in the non-ego, which are related to the ego in like 
modes, necessarily occupy heterical wheres. Each of these wheres may 
be but a single point, which can not be resolved into hetera; but the two 
wheres must be separate, and if they be. separate, that which separates them 
w r e call space. Space is a truth which forms a class of truths by itsdf 
alone. Wheres are necessarily resolved. into hetera, when we resolve exist- 
ences grounded in the non-ego into hetera, i. e., existences grounded in the 
non-ego can not be so resolved without heterical wheres. When we re- 
solve .existences on the other hand, which are grounded in the ego and pro- 
duced by the ego's action in the same mode and direction, into hetera, we 
necessarily resolve times into hetera. Time also is a truth, which farms a 
class of truths by itself. Mr. HunVe derives our knowledge of space from 
color. And if a color cover sufficient space to be resolved into two or more 
some wheres, space will be evolved from the relation of those wheres : but 
if only a single point of color so minute as to be incapable of being so 
resolved, be presented, no knowledge of space can be gained from such" point 
per se. Mr. Locke obtains all our knowledge of space from both touch and 
color, and ttiis may also be done in the manner we have stated. Sir Wm. 
Hamilton calls space "A native idea ot the mind," which expression seems 
to have no meaning. 

We have now shown how we derive and classify our knowledge of 
colors, tastes, scents, touches and sounds, and of acts of the mind itself into 
hetera, of ordinal, cardinal and temporal numbers, and of time and space. 
And it will be seen that existence, not as a class distinguished* from other 
things, but as the state of being in contradistinction to non-entity, stands at 
the head of our inquiries. Existences are then divided into perceptional arid 
self-conscional facts, and from the relations of these we evolved conscious 
truth?, our first class of truths. We then found some conscious truths to be 
grounded in the ego and others in the non ego, and in each of these classes 



29 
we found nominal truths, so called because they are the first truths which 
receive differential names. From the relations of nominal truths inter se\ 
we then evolved primary propositionai truths, so called because they are the 
first truths which can be used in propositions in which the words no, none 
and not, do not occur, and in which the subject and predicate terms are not 
the same name. We then evolved secondary propositionai truths, and saw 
that w£ had exhausted those simple existences which hereafter* we will call 
facial gregaria. We then evolved the ordinal, cardinal and temporal num- 
bers and time and spate. And we must still proceed further with our in- 
quiries before we commence where logicians have usually commenced in 
treating of the reasoning processes. But if the reader will have patience to 
follow us in our preliminary inquiries, we believe, he will be able when we 
come to treat of propositions and the syllogism, to understand the whole 
matter, and to escape from the obscurities and perplexities, which in our 
opinion, have hitherto surrounded those subjects. 

CHAPTER VI. 

, CLASSIFICATION OF AGGREGATE EXISTENCES AND OTHER TRUTHS. 

Having already considered those simple existences grounded in the 
non-ego, which we shall call facial gregaria, we come now to the contem- 
plation of aggregate existences. We may find a color, a s#und, a taste, a 
touch and a scent, all situated in one location. Two existences grounded in 
the n©n-ego and related to the ego by the same mode, can not occupy the 
same where at one and the same time : for if they do, the existences can not 
be hetera. Thus : two colors can not exist in the same w r HERE,nortwo sounds, 
nor tastes, etc., at the same time. But the five nominal truths grounded in the 
non-ego, nevertheless, may all be found co-existing at the same time in the 
same where and forming the facial gregaria of an aggregate existence (Gre- 
garius, a, um ; gregaria, neuter plural— things in a herd). And by an aggregate 
existence we mean an existence composed and made up of simple existences; 
as the leaf of a rose, iron, snow, a stone, water, etc. These aggregate existences 
grounded in the non-ego possess facial gregaria, some, if not all of the nominal 
truths grounded in the non-ego. 

But aggregate existences, besides the facial gregaria,have also capacial 
gregaria, i. e., capacities to receive and give effects among themselves. If we 
move two heterical and aggregate existences towards each other, we find that 
both can not be made to occupy the same where in space at the same time ; 
one of them must necessarily exclude from its where, the other, or they 
both could not remain hetera. This capacial gregarium of aggregate exist- 
ences is called impenetrability, and is said to be one of the primary properties 
of matter. And each particle of matter must necessarily have a where in 
space and without a where it must cease to be an existence. Impenetrability, 



30 
therefore, is one of the essential capacial gregaria of aggregate existences : if 
matter did not possess impenetrability each particle might annihilate its 
neighbor until the earth became a lion-entity. And another essential capa- 
cial gregarium of aggregate existences is form or figure. 

But after we have gained a knowledge of matter, i. e., of aggregate 
existences, we readily perceive that in some matter the particles cohere 
rigidly, while in others they move freely among themselves. This eapacial 
gregarium of the one and that of the ether are inter se differentia: and if we 
distinguish these gregaria inter se we will have the classes, solids and fluids. 
Then again fluids may be discriminated by their facial and capacial gre- 
garia: one will not have a like color with another, and their tastes may be 
differentia: a volume of one may be tried in a balance with an equal volume 
of another, and their specific gravities be' found to differ : heat may be applied, 
and fluids be found to differ in the degrees of heat necessary, ceteris paribus, 
to make them boil, etc. And wherever the mind can discriminate into differ- 
entia, it will form classes of fluids; and those which are not to us differentia, 
may be called by one and the same name. The knowledge of all classes ol 
fluids is gained by differentiating their gregaria either facial or capacial: capa- 
cial as well as faoial gregaria being truths grounded in the non-ego. 

And when men begin to examine matter closely, they find that the 
particles composing one bulk may be analyzed, i. e v discriminated into differ- 
entia. 'And hence they form classes of what they call elementary substances, 
i. e., aggregate existences, the particles of which can 'be discriminated into 
hetera, but not into differentia. The ancients knew but four elements, viz : 
earth, air, fire and water: man has since found a great many more elementary 
differentia. And every differentiation, that the mind can make, throws new 
light upon the world and adds new truths to our store of knowledge of the 
elements. Now the number ot facial gregaria that matter may possess, so far 
as we can know, when expressed in the classes of nominal truths, is five. 
Each of these five classes, however, are divided into numerous primary pro- 
positional truths, which have names, and besides these there are various 
other classes of which we have knowledge but for which we have no names. 
But the number of capacial gregaria of matter is found out slowly, one 
after another : and where the number ends we can not even guess. Each 
generation to come may find out new capacities of matter, and when they do, 
they will ot course make new classifications according to the differentia dis- 
covered. We have matter, now, classified by its specific gravity, its attraction 
of cohesion, its friability, its ductility, its maleability, its compressibility, its 
effects received and produced among existences, etc. Any capacial gregaria, 
which are inter se differentia, may produce classes of matter. Chemestry is 
a succession of differentiations of elements and compounds, i. e., capacial 
gregaria discovered by experiment. And what is very strange, the mineral 



31 

enter into compounds in a binary manner, as truths are compounded, so to 
speak, in a proposition as we shall see by and by. Thus: carbon and oxygen 
unite and form carbonic acid: hydrogen and nitrogen unite and form 
amonia: and then the carbonic acid and amonia unite and form the carbonate 
of amonia. Now the mental process of similatingand differentiating hetero, 
gives us all the classes, which we possess, of the different kinds of com- 
pounds and elements. The classification of matter by differentiating its 
capacial gregaria, so far as it has been accomplished, may be found in works 
on chemistry and materia medica. And we must perceive that aggregate 
existences when stript of their facial and capacial gregaria, are unknown to 
us. The gregaria are the only things of which we have any knowledge 
through the senses. That which lies behind the gregaria are merely infer- 
ences drawn from the gregaria. 

Now after knowledge has increased and language been invented to ex- 
press it, the science of grammar takes its rise. Men begin to similate and 
and differentiate words. The parts of speech are classified by differentiating 
the intentions of the mind in using different words, i. e., by the functions of 
words. The principles of the declentions of nouns and adjectives, and of the 
conjugations and inflections of verbs are obtained in the same manner. The 
knowledge of tense is gained by the discrimination of .times into lietera: of 
modes by the differentiation of manners and so on. 

The same mental process also obtains in Botany. The botanist differ- 
entiates, cotyledons, radicles, plumules, etc., and as the plants grow he finds 
buds, which he in like manner classifies into auxiliary, accessory, adventi- 
tious, latent and so on, he also differentiates the leaves and give distinguish- 
ing names to each class. The whole classification of botany, shows, that the 
human mind has been dealing with every part of the plant by similatingand 
differentiating. 

And if we look into Zoology, the same mental process meets us at the 
threshold. Vertebrated, radiata, articulata, rumenants, pachydermeta, planti- 
grade, etc., are classes obtained by the differentiation of truths. And this can 
easily be shown to be the case with ethnolog}^ entomology, mineralogy, 
anatomy and all of the natural sciences. And hence, each of those sciences 
is also a mental philosophy giving us the classifications of as many truths 
as the particular natural science contemplates. Accepting therefore the 
classifications of the several natural sciences and making them our own, we 
will proceed to consoler other truths, which come to our knowledge from 
other sources. ■ - 

After having obtained the knowledge of space and matter, we may 
easily get the truth of extension. Extension, indeed, independent of every- 
thing else has no existence: it is not -a consious truth. We speak of the 
extension of srmce and that of matter : but had there existed nothing extended 



4 

32 
extension could have made no part of our knowledge. And whatever is ex- 
tended must be so extended that two points in space, two somewheres, can 
he discriminated by the mind. And hence extension when applied to matter 
means consecutive and contiguous points, which can be discriminated? And 
in every other sense, the word is misapplied ; and it is thus when we use ex- 
tension as synonomous with space. The proper meaning of the term exten- 
sion is the stretching out of something. And if we take two points and con- 
sider the space between them, and then remove one of the points further from 
the other, the space between them will be extended. So if we consider a 
colored point on paper, the enlargement of that point will extent the area of 
the color. A mere mathematical point can not give us the knowledge of ex- 
tension: but two mathematical points separated from each other, can give us 
the knowledge of the extension of space. Our knowledge of extension is 
gained by the discrimination of heterical points located in something in 
space, or in space itself. The consecutive points must all be in some exist- 
ence of the non-ego: for extension is a truth gained by the comparison of 
truths grounded in the non-ego. Extension, like time and space, forms of 
itself but one truth and a class of truths^ i. e., there may be heterical exten- 
sions but the hetera are inter se similia; there may be heterical times and 
heterical wheres, but inter se times are similia, and so of wheres, and there- 
tore, each makes but one class. 

But again, if we take an aggregate existence, a piece of iron for 
instance, and move it to another palce, we will perceive that it is not now in 
the same where in which it w T as before it was moved, it has changed its 
place in space. And hence the heteration of wheres occupied at differ- 
ent times by one and the same existence, gives us the knowledge of that 
existence's motion. While the same points in an existence remain in the 
same wheres, no discrimination of any points wheres, of course, can be 
made, and without the heteration of one and the same point's wheres, no 
motion of that point can take place. This truth of motion, again, forms of 
itself a class of truths. 

But again: we have in our minds testimonial truths. And testimonial 
truths are those, which we receive upon the testimony of others without 
bringing them up from facts for ourselves. And every witness must testify 
to that only which has come under his own observation, or to a truth which 
his own mind has wrought out: or, if a person state that which has been 
told to him by another, and the other but related* what he had heard, in 
order that there may be any truth at all in the story, there must have been 
some person, whose mind brought the truth in question up from facts. For 
some truths, we are entirely dependent upon the testimony of others: as that 
Caesar was assassinated, Columbus discovered America, etc., while there are 
others, which w T e may gain for ourselves from nature and also receive them 



from testimony: as that the sua and moon shine upon China. And respect- 
ing those truths, which are conveyed to our minds by the testimony of others, 
it is to be observed that there must always be.some analogy in the whole or 
in tne parts, between a#tauth related to us and some truth of which we already 
have the knowledge: otherwise we can gain no knowledge by such relation, 
should there be no analogy existing between the truth, which a friend desires 
to relate to us, and some truth with which we are already familiar, no con- 
ception of the truth in his mind can be established by words in our own. 
The king «f Siam is said to have laughed when told that water, a fluid, would 
congeal and become ice, a solid : but if he had had already no knowledge of 
a solid or fluid, he would have had nothing at wdiich to laugh: for he could 
have known nothing about the subject of the conversation. If a traveler 
should discover in some unexplorifl country an animal with feet like those, 
of a cow, a body like that of a lizzard, and a head like that of a crane, by 
using these things with which we are familiar to explain the appearance of 
the various parts of this newly discovered creature, he could give us a con- 
ception of his animal as a wholg. But should a traveler discover an animal, 
which in the whole and in the parts, was entirely, unlike anything of which 
we have any knowledge, he could not possibly, by language, give us any con- 
ception of what he had seen. And in order that we might gain any knowl- 
edge of puch an animal, we would have to see the animal itself, or have a 
picture or sculptured image of it presented to us. 

But again: we have the knowledge of existences of the imagination. 
These existences are peculiar and require some consideration here. Centaurs, 
Sphinx, Harpies, Hydras, etc.-, are represented to us, while these creatures 
really have had no objective existence in nature. Yet the mind per se has no 
power to create from nothing existences of any kind; even the baseless fabric 
of dreams is not the' creation of the-mind from nothing. But if existences 
of the imagination have no real objective existence, and if the mind can not 
create them from nothing, whence do they come to be subjective existences? 
The state of the case is this, a centaur, and all other existences «of the imagi- 
nation, though they have no real objective existence in nature as a combina- 
tion and whole, yet all of them, partially in the parts considered, have a real 
objective existence. A centaur is an existence of -the imagination, one part 
of which is like that of a man, and the other like that of a horse. Both of 
the parts separately considered, have a real objective existence in nature. 
The imagination unites these parts and from their c^inbination creates an 
existence, which has a real subjective existence, but which as. a whole, a 
unity, has no objective existence. But had the parts, separately considered, 
no objective existence, their unity could never have had a subjective exist- 
ence. Ail the imagined monsters of ancient and modern times have been 
formed in this manner. The images in works of fiction, the Gods of fiomer, 



34 V 

the Metamorphoses of Ovid, and the character of Hamlet and Othelo are 
creatures of imagination, which have been collected in the same manner. 

CHAPTER VII. % 

CAUSE AND EFFECT. 

As we will have occasion in a subsequent part of this volume to treat 
of cause and effect, it seems necessary to prepare the way by examining the 
manner in which we come by the knowledge of these existences. Now we 
can gain no knowledge of cause except through effect. We may know 
arsenic as a metal ; but as a poison, a cause of death to animals, we can 
know nothing of it without first having the knowledge of the effect; thaj; 
this capacial gregarium is . contained in it, is found- out through the effect. 
We can not view objects, which are poteffftai causes, and per se determine 
such to be their case, a priori ; it is some effect of which we first gain the 
knowledge, that brings to our minds the knowledge of cause. But the 
very instant we look upon anything as an effect, we have the knowledge of 
cause: for, cause and effect are but counterforts of each other. To under- 
stand, therefore, what we mean by cause, it is necessary to begin with the 
examination of effect. 

Now an effect, in general language, is some change produced,, With- 
out change there can be no effect. If we conceive of the earth as having 
always existed, we can not conceive of its .existence as an effect. We do not 
mean liowever, that that of which we can not conceive, can have no existence : 
all we mean is that we can have no knowledge of that of which we can not 
conceive. And if no changes whatever took place upon the earth, or in the 
heavens over our heads, we could never gain the knowledge of effect, and 
consequently we could know nothing of cause. If we consider pure space, 
we will see that we can not conceive of its having had a beginning, or of any 
changes whatever having taken place in its nature, and therefore, we can not 
conceive of it, as an effect. The knowledge of change must preceed that of 
effect and cause : and when we perceive that the change has been produced 
by something else than the change itself, we then have the knowledge of 
effect and cause. We must perceive, however, that the change has been pro- 
duced, or we do not come, to look upon such change as an effect. Suppose 
the flrst inhabitants of earth to have looked upon the moon and to have seen 
her undergoing in appearance, continual changes, (and this they could not 
have avoided if they Rooked up) could they have evolved the truths of effect 
and cause fr©m these phenomena alone? We think they could not. If lie 
first changes with which men became acquainted were those of the phases of 
the moon, and their minds were not yet familiar with the exertion of any 
power in nature to produce change, providing they really believed the old 
and full moon to be in reality changes in the same moon, indicated by 



85 
phenomenal differentia, the comparison of these differentia would only 
evolve the knowledge of change. But that this change was the effect of 

• some cause, could not be evolved from such comparison. 

Now the simplest. change with which we are acquainted, and which 
we can perceive to be produced, to be an effect, is the change of aggregate 
existences in space; i. e., a change of their wheres. ^ Suppose a man should 
see one ivory ball strike against another and send that other some distance 
through space; in such case he would see a change produced, an effect. He 
would perceive heterical wheres occupied at different times by the one and 
same ball wlfich was struck, and also heterical wheres occupied successively 
by the striking ball: he would also perceive that soine ef the heterical 

, wheres of the one ball and some of those of the other, became, at different 
times, homon (Greek— neuter singular; from homos, a, on — the same). If we 
contemplate the two* balls, we perceive that they are hetera*and that their 
where* are hetera ; and w*hen the striking ball moves towards the other its 
course is made* up of wheres which are inter se hetera until it strikes, when 
the ball struck makes heterical wheres. But so soon as the first ball strikes 
the second one, some of the first one's wheres and some of the second one's 
whefes become homon, and from the impenetrability of matter, this could 
not be the case without the second one having vacated those wheres. In this 
case the change in space of the second ball is seeSto be an effect, and the 
cause is easily perceived. The first ball commenced to move towards the 
second one until it touched it, and had it proceeded no further, no effect 
-would have been produced upon the second one: but if it go on further, 
some of its wheres and some ot those of the second must become homon, i. 
e., the wheres of the second hall at one time and the wheres of the first ball 
at another time, are in space, homon. Now one instance of change involv- 
ing such relations, if contemplated, would give us th« knowledge of effect 
and cause. 

But again, if we tie one end of a string to a permanent object and 
attach the other end to the one end of a lever, every point in that string will 
occupy a where, and the w T heres of all the points inter se be heteTa. The 
end of the lever to which the string is attached will also have a where, which, 
in reference to any point in the string, "will be heteron. If now the string 
contract, some of the points in the string will take the wheres of other points, 

* and some of the wheres of the end of»the lever, and some of^the wheres of 
points in the string, which were at first hetera, now become homon. And 
hence we see that in all those changes of aggregate existences in space, which 
we regard as effects and whose causes we understand, we find heterical ex- 
istences with heterical wheres, and some of the wheres of one and of another 
becoming homon. Change of objeets in space is also produced by what is 
called attraction and repulsion, but what are flie causes and modus operandi 



36 
in these changes^philosophers have not yet sufficiently explained to us. The 
convertion of hetera into homon among wheres, is the modus operandi in 
those changes of objects in space, which we fully understand. Take a piece 
of iron and keep it all the time for a certain period under your eye, and 
during this period move it with your hand from one place to another. In 
this case we perceive thttt the existence moved (the iron) remains one- and the 
same ; but its wheres successively and the times of occupying them can be 
discriminated, and so also respecting your hand. But some of the wheres 
of the iron and some of the hand's wheres can not be discriminated, they are 
homon, though the times of occupying them by each successively are never 
homon* always but hetera. 

But again, .we sometimes see one existence acting upon another, and a 
constitutional flange following such action. Take a hammer and with it 
strike a grain of corn placed upon a rock, and we will see that a constitu- 
tional change takes place in the corn. This change too, we could scarcely 
avoid regarding as an effect the first time that we should witness the occur- 
rence. And in this case, it will be perceived that two heterical existences 
come in contact and that «some of the wheres of the one and some of the 
ether become homon : and further that some of the heterical wheres of the 
particles in the grain of^porn become homon, and hence the constitutional 
change. The grain of corn possessed rigidity but this gregarium was cle- 
stroyecf by reducing heterical. wheres of heterical particles to homon. On 
the contrary ignite gunpowder and heterical particles immediately take 
heterical wheres. ♦ 

Again, if we take a piece of ice in our hand and it melt and become 
water, here is a* constitutional change; ice, an aggregate existence, has 
changed some of its -sjregaria and become water : and in changing these 
gregaria, heterical wheres ot particles became homon. And in this case we 
must perceive that the where of the two aggregate existences, ice and water, 
remains the same for both; but the existences possess gregaria inter se differ- 
entia, and the times of occupying the same where are hetera. And hence, 
when there is during a certain period of time but one where for two differ- 
ential existences, the one must have occupied that where for a part of that 
period and then become the other existence. And when we conceive such to 
hav*e been the ckse, we can not help conceiving of a constitutional change 
having taken place. Now in change times can always be heterated and when 
we can go a^ step further and heterate wheres, the change is that of place. 
But when we can go still further and perceive that an aggregate existence 
has lost some of its gregaria and taken others, which with reference to the 
first are differentia, the change is constitutional. A piece of iron when heated 
possesses different gregaria from those which it has when cold: this is owing" 



37 
to a constitutional change. It, however, cools sfgain and assumes its former 
gregaria. 

But again, if we take grains of white sand and consider them all to- 
gether in a pile, we shall have a honiogenious aggregate existence, L e., an 
existence in which all the particles are inter se similia: and consequently 
the wheres of all the particles can he heterated but the particles themselves 
can not be differentiated, if now we mix red sand with the pile, we then find 
in it particles which are not only hetera but also differentia. The pile now, 
therefore, compared with what it was shows change. This change, however, 
is owing entirely to the change in space of the particles of red and white • 
sand. 

But again, suppose we take an aggregate existence in which all of the 
particles are similia, so far as we can perceive, but by subjecting it to a certain 
process we find that particles which we regarded as similia have become 
plainly differentia, which is always the case in the anal} T sts of compounds, 
here is to us a change of a different kind from any of the former. 

And again, suppose w r e take two aggregate existences, in each of which 
the particles inter se are sitnilia, but the particles of the one aftd those of the 
other are inter se differentia, and we put these two aggregate existences to- 
gether and find that all the particles of each existence now, if compared with 
what they were then, are then and now intense differentia, but among them- 
selves theyjiave all became now similia: here again is a change different in 
kind from any of the former. This change always takes rnace when differ- 
ent elements unite and form a compound. 

The following:, therefore, appear to be the princi|fel changes with 
wiiich we are familiar, viz : the starting an aggregate existence in an homoni-' 
cal where into heterical wheres, which is a change of place ; the change 
of heterical wheres of particles into homonica! wheres, and vice versa, which 
is a constitutional change of the adhesion of particles inter se, as in crush- 
ing and expansion; the convertion of similia into differentia, which is the 
analysis of a compound; and the conversion of differentia into similia, which 
is the synthesis of elements, having chemical affinity f©r each other; Every 
change which takes place among existences of the non-ego involves the prin- 
ciples of one or another of the above examples, excepting changes in degree. 
And we can readily see that one homonical existence per se can not chaDge, 
but that the change of any one existence is owing in part to some other exist- 
ence. Every change is dependent. And as change springs from the relations 
of existences, w T ithin those relations must also be the cause or power to pro- 
duce change. Sodium pers se does not posses the cause of soda; nor does 
oxygen contain it within itself; but from the relations of sodium and oxygen 
spring the protoxide of sod aim or soda. And we see that the knowledge of 
change comes into our minds by^coinparison : and so also does our knowl- 



edge of effect and cause. Ami without the involution of homon and hetera, 
or similia and differentia, or commensura and incomensura, we can not evolve 
the knowledge of cause and effect. 

There is a change in the appearance of the moon ; there is also a 
change in the s-tate of the atmosphere, by the comparison of these changes, 
we have hetera and differentia; but neither homon or similia.. And from these 
things per se, i. e., from hetera and differentia, or from homon and similia, or 
from hetera or homon and commensura, we cannot evolve the knowledge of 
cause and effect. If a rock fall from the cliff of a mountain into the valley, 
•and about the same time the ice break loose from the shores and float down a 
river, here also are changes, but they do not come together anywhere, so as 
to bring hetera into homon, <5r vice versa ; similia into differentia, or vice" versa ; 
commensura into incommensura, or vice versa; so that we can evolve from 
their comparison an effect or cause. Hetera must meet somewhere in homon 
or vice versa; or similia in differentia, or vice versa; or commensura in in- 
commensura, or vice versa; in order to bring to our minds effects and 
causes. • 

Now of Causes there are three classes viz: expended, acting and poten- 
tial. Causa striarum of the rocks is an example of an expended cause. The 
floating icebergs, as believed, striated in their course the rocks. But 
they have vanished and ceased tc^ be causes. The flowing of the water in the 
river is an effect of an acting cause, and gunpowder unexploded ^ an exam- 
ple of a potential cause. 

» CHAPTER VIII. 

NAMES^ 

We come now to the consideration of names. When we reason and 
use words, we must necessarily see to it, that our words have some definite 
meaning, otherwise we wall but veer about over subjects at random without 
making comparisons in such a manner as will evolve truths. In the most 
common affairs of life we reason either well or or ill, and we lead others into 
our trains of thought and reasoning by the use of words. So much have 
•words to do with reasoning, that Archbishop Whately concluded logic, or the 
science of reasoning, to be entirely conversant about language: a mistake 
similar to that of supposing the symbols of Algebra to be the only things 
about which that science treats. But the relations of existences inter se are 
subject-matter of the science of reasoning and of every other science. And 
as words are used to designate the results of these relations, the -words them- 
. selves must subjectively bear some relations to each other and to the exist- 
ences which they are used to designate: and "so far as they are brought by 
the mind to play a part in the relations of the ego to the non-ego in reason- 



ing, they are the subjects of the science of reasoning. And after what has 
already been said in the previous chapters, we do not thing it will be very 
difficult to undeastand the functions of words in the processes of reasoning. 

We have already seen, that hetera lie at the very foundations of r our 
knowledge. That which is so related to the ego, that it may be an object 
between which and the ego, some truth depending upon such relation may 
come to our knowledge, we call an existence. And words when spoken are 
to the ear signs of cognitions of the person speaking them; when written on 
paper they are signs for the eye. And when existences come to our knowl- 
edge to be existences by the power of the mind to evolve the relations among 
which it is placed into hetera, these heterical existences are known only as 
hetera, and no one of them is distinguished from another except as separate 
existences. And when we consider one of these heterical existences inde- 
pendently of its relations to others, and we wish to set out a word as the sign 
of our cognition, we use a name to call to the mind of the hearer or^f him 
who sees the word written, one of hetera, without distinguishing in any 
manner this one from others. 

And hence words, for logical purposes, may be divided into two 
classes, viz: names which are used by us to distinguish existences inter se, 
and names used to call to the mind existences without distinguishing them 
inter se. To the later class belong such words as existence, being r thing, 
entity, phenomenon, etc. These non-distinguishing names are few in number 
in all languages. And taking up the second class, i. e., names used by us as 
signs to distinguish existences inter se, we will notice those few in number 
which distinguish hetera inter se. Names to distinguish hetera inter se are 
such words as the following: this and that, these and those, once, twice, first, 
second, ego and non-ego, etc. 

But every conscious existence has a where, which it occupies, and the 
relations of wheres occupied by conscious existences are expressed by prepo- 
sitions. The where, however, and the conscious truth which occupies it, are 
differentia. And we will, perhaps, be letter understood if we sub-divide 
that class of names, which distinguish existences inter se, into six classes, 
viz: names of homon,of hetera, %f similia, of differentia, of commensura 
and of inconimensnra; and keeping this sub-classification in view, we will 
treat of them somewhat promicuousiy. m ■ 

Now it must be evident that sometimes a simple word is used as a 
name, as iron, glass, ice, etc, and sometimes names are compound words, as 
hydrophobi?, etc. All those word§, which by grammarians are distinguished 
'as noun|, are names. Some of these are names of simple existences as red, 
taste sound, etc,, and some are names of aggregate existences as iron, wood, 
coal, ship, etc. And all those words too, which are grammatically adjectives, 
are logically but names. of the gregaria of aggregate existences. In the ex- 



pression, "A red house," the word red shows that this facial gregarium is 
one*of the gregaria of the house, and of this facial gregarium, it is the 
name. • And all adjectives of the positive degree when joined to aggregate 
existences, name some one of the gregaria, facial or capacial, which along 
with others constitute the peculiar aggregation named by the noun to which 
the adjective "belongs. In the expression, "A good man," the noun man is 
the name .of an aggregate existence,- and the word 'good,' which ip joined 
with it, is the name of one of the capacial gregaria supposed to be in the 
aggregation. "A fusible metal," is an expression of thefsame kind. And it 
is to be remarked that those adjectives which are the names of facial gre - 
garia may. stand alone as the names of either the subject or predicate of a 
proposition: while names of capacial gregaria require, generally, in our 
language, the names of existences in which • the gregaria named by *them 
severally, are aggregated, to go along with them when they are made the 
subjec^of a proposition. We can say that white or red is a color; but we 
can not say tkat a round is on the table, and we should rather say a round 
thing is on the table. And when we wish to use such words, which are the 
names of capacial gregaria, as names»by themselves in the subject of propo- 
sitions, we usually change the form of the word: thus round is changed into 
roundness, rectangular into rectangularity, heavy into heaviness or weight, 
etc. . 

The article a or an is continually used in logical propositions and it 
always has a significance. This article is the name of an heterical relation : 
it is derivecrfrom ane; German ein, and means one. And therefore, the 
expression, "A red house," contains three names viz: house, the. name of an 
aggregate existence ; red, the name of one of its gregaria, and a (one), the 
name of the numerical relation of the house. The article the, is the name 
of an homonical relation, and it is used to distinguish homon from hetera: 
as, "This is the horse which we saw yesterday," "Thou art the man," etc. 
Sometimes the adjective same and also the word self are used along with the 
noun to which the article refers : j^s, "The same horse," "The gate itself." 
The articles, however, can not be used alone, either as the subject or predi- 
cate of a proposition which is concerned* about anything else than names. 
They, however, frequently appear in propositions along with other names, 
and their functions, therefore, ought to be understood. 

Prepositions are the names of relations among existences and among 
the wheues of existences in space : as, "The log under the bridge," "In the 
house," "Over the river," "Beyond the tree," etc. Adverbs are the names of 
relations of time and space and modes of acting: as here, there, thjn, now, 
bravely, dilligently, etc. We do not propose to treat of woitfs any further 
than it is necessary to the understanding of reasoning, and we hav« perhaps, 
said enough about simple names for the present. 



41 

But frequently several words taken together make but one distinguish- 
ing name: as "A red color" is the name f)f a single and simple existence. 
Again, "Charles Carrol of Carrolton" is but one name. And u The miller 
who ground the grist yesterday and who died to-day" is but one name, and 
after it we may add, "was a man of benevolence," another name. "In the 
house" and "By the sea-side" are flistinguishing names of heterical wheres. 
Such names are called by logicians many worded names. 

But again, a collective noun oy name stands as a sign to distinguish an 
aggregation of aggregations: as, the assembly, a multitude, a battallion, 
regiment, etc. And when such names are used, it is usual and frequently 
better for the sake of perspicuity, to connect the name of an aggregate exis- 
tence, which with others of the same kind make up the collective aggrega- 
tion, with the collective noun: as the assembly of the people, a multitude of 
women, a regiment of geese, a society of prairie dogs, etc. 

Again : a geneial or common name is one used in the first instance to 
distinguish an individual existence, either simple ©r aggregate, which has 
been differentiated or incommensurated from others: but each of those exist- 
ences, which, with the first existence named are samilia or commensura, 
must receive the same name, and therefore the name becomes general or 
common. A common name is the name of similia or of commensura. Ex- 
istences inter se similia never receive a name other than a common one for 
each inAvidual, for the simple reason that, after we have distinguished them 
into hetera there is nothing by which we can distinguish them further. We 
may call them 1st, 2d, 3d, etc., but such naming distinguishes them merely 
into hetera. And in order that any existence may be given a name to dis- 
tinguish it from others otherwise than hetericalty, it and the others -must be 
inter se differentia. If we take ten grains of corn inter se similia, and call 
one Alpha, another Beta, another Gamma and so on, our naming has amounted 
to nothing; for so soon as our eyes are turned away from them and they have 
changed places, we can not afterwards tell,, which one is Alpha or Beta, etc. 
All those existence^, therefore, which can not be discriminated by us further 
than into hetera, must from a mental necessity, when not numerically con- 
sidered, receive from us a common name. But it may be said that horse is 
a common name, yet horses can be discriminated. This is true, and then 
they also receive distinguishing names; not indeed, to distinguish the indi- 
viduals from objects, which are not horses, for the name horse has already 
done that, but to distinguish them inter se; as black horse, white horse, 
Arabian horse, the horse with short ears, the near horse, the off horse, etc. 
In like manner color is a common name, yet colors inter se can be discrim- 
inated into differentia, which receive distinguishing names, and which names 
may also be common names, and they will be, if any color, discriminated 
from others, have similia. 



42 

Now if a man should place before himself a horse, a tree and a stone, by 
examining them, he would perceive, that the one possessed the capacial grega- 
rium of animation ; the other the capacial gregaria of vegetation, and the 
last, capacial gregaria of a different kind from either of the former. These 
three objects, therefore, would be inter se differentia : they are the three 
aggregate nominal truths, and we may distinguish them inter se by the 
'names animal, vegetable and mineral. And afterwards every object possess- 
ing the capacial gregarium of animation and the horse, as aggregate nomi-^ 
nal truths, would be similia, and' therefore it must be called by the name 
animal. Animals, however, may be differentiated into aggregate primary 
propositional truths, and so on in a like manner, which, we saw was persued 
with those sirriple existences, which we call facial gregaria grounded, in the . 
non-ego. And it must appear, that if every aggregate existence, with which 
we are acquainted, possessed the like numbed of facial and capacial gregaria, 
which were inter se similia, aggregate existences could only be discriminated 
into hetera, they would all be similia and they could have but one common 
name. But the facial gregaria inter se differentia are many and the differ- 
ential capacial gregaria are innumerable; and could we Jfmd an aggregate 
existence, in which all the facial and capacial gregaria excepting one were 
like those of gold, yet as it differed from gold in one respect, it and gold 
would be differentia, and consequently it would have to receive a^name to 
distinguish it from gold and other tilings. Common names, therefore, are the 
names of the individual existences severally, which upon one and the same 
generalization of existences are similia or commensura. 

A proper name is the name given to a single existence to distinguish it 
from all others in the universe. And it must be perceived that, besides the 
capacial gregarium of animation, which distinguishes animals, animals are 
made up of various other gregaria, both facial and capacial, by which we 
can easily distinguish them inter se. And after that we have sub-divided 
them into species, we are still able to distinguish the individuals of the same 
species. Take for instance, the. species or genus homo, and after that we 
have divided this species into the five races, we can easily distinguish the in- 
dividuals of the same race. Nature is so fond of variety that, in the largest 
cities two men can seldom be Tound, who are in all respects similia* And 
this variety of gregaria outride of those upon which the generalization, in 
respect to which men are similia is made, enables us to impose with effect 
proper names upon individuals. Daniel Webster, outside of those gregaria 
which made him and other men inter se similia, possessed gregaria facial and 
capacial, by which he could be^clistinguished and known from others. City 
is a common name, and yet every city, besides the juxtaposition of houses 
and the jostling of men, has other relations and dissimilar plats and surround- 



43 
ings on.the earth by which we ma}' distinguish them by the proper names 
London, Paris, Philadelphia, etc. 

Correlative names are the names of existences so related to each other 
"that the mention of the one suggests the relation : as father and son, hus- 
bantl and wife, mother and child, cause and effect, king and subject, etc. 

A concrete name is the name *>f an existence grounded in the ego and' 
considered with reference to its ground in the ego, or of an existence ground- 
ed in the non-ego and considered with reference to its ground in the non- 
ego ; in other words the existences (for, names in themselves can not be con- 
crete or abstract) distinguished by what are called concrete names, have 
their Iccations in the ego or in the non-ego, assigned to them by the mind 
when their name are spoken, and therefore, the}" are concrete; and from this 
circumstance the names of such existences are called concrete. An abstract 
name is the name of an existence for wiiich the mind assigns no location, 
but merely views the existence subjectively without determining its ground 
either in the ego or non-ego, as whiteness, fusibility, roundness, etc. The 
adjective names of facial and capacial gregaria, such as white, red, sweet, 
' fusible, combustible, conscious, etc M are generally concrete; and when the 
existences for which they stand are.to be view T ed in the abstract, we change 
these names grammatically into nouns: as whiteness, redness, blackness, 
consciousness, etc. We may however use abjective names to denote abstract 
existences, as white is not black, i. e., whiteness is not blackness. 

Karnes have been divided into positive and negative. This division, 
ho^vever, is made altogether from the combination and appearance of words, 
and not from the functions of word§ as names. The division made by Aris- 
totle into definite and indefinite is a much better one: as definite white, red, 
man, horse, etc. ; indefinite not-white, not red, not man, etc. Definite names, 
then, are names of individuals separately, or of the individuals severally of a 
class; and indefinite names are the names of anything not denoted- by the 
definite name, which is always part of the word used as an indefinite name. 
The truth is that such name's as not red, not man, nothing, non-entfty, etc., 
can have no existence in any language independent of propositions, they 
Spring up in propositions, and in order to understand them, we w 7 ill have to 
treat of propositions. There is also another set of names, such as blind, 
mute, deaf, etc., which liave been called privitives; they certainly exercise 
the functions of names, but we can understand tUj£in much better after hav- 
ing treated of propositions. It has been usual with writers on logic to treat 
explicitly of names and their divisions, and we have said this much by a 
kind of duress, although after names have been divided into names of hetera, 
homon, similia, differentia, commensura and incomniensura, we deem the 
otfrer divisions of no great importance. 



44 

Note.— — It seems necessary at the end of this chapter to notice 
briefly, what we regard as erroneous in the chapter on names in the work of 
J. Stuart Mill on logic; not because we wish to find fault with Mr. Mill 
more than others, but because Mr. Mill is one of the strongest writers upon 
logic in the English language, and the futility of the' subject is, therefore, 
best shown from his wjorjg. On page eighteen, of the edition pubHslr%d by 
Harper & Bros., he says, " A general name is familiarly defined, a name 
which is capable of. being truly affirmed in the same sense of each of an in- 
definite number of things. An individual or singular name, is a name, 
which is only capable of being truly affirmed in the same sense of one 
thing." And again on the same page, "A general name is one which can be 
predicated of each individual of a multitude; a collective name can not be 
predicated ot each separately, but only of all taken together." Now upon 

. the foregoing, we would remark that a name can not be affirmed of any- 
thing; for, every expressed affirmation is contained in a proposition, and 
that, which is affirmed in any proposition, can not be a name, as we will see, 
when we come to treat of propositions in chapters X, XI, XII, XIII, XIV 
and XV. Mr. Mill, in his explaination of names has all the time had in 
view the generally, we may say, the universally received hypothesis that, in 
propositionsjlie predicate term is affirmed or denied* of the subject, or that 
the thing denoted or connoted, to use a term of Mr. Mill and the schoolmen, 
by the predicate term is affirmed or denied of the thing denoted or connoted 
by the subject-term ; a theory which we hope to be able to show hereafter to 
be entirely erroneous, and which has led Mr. Mill and other eminent writers 
into erroneous conceptions of names. But again on the same page as be- 
fore, "A concrete 'name is a name which stands for a thing; an abstract 
name is a name which stands for an attribute of a thing." And hence the 
name of an attribute of a thing, is the name of nothing, unless an attribute 
be a thing of a thing. Button page thirty-two he tells us that, "When we 
have occasion for a name which shall be capable of denoting whatever 
exists, as contradistinguished from' non-entity or nothing, there is hardfy a 
word applicable to the purpose, which is not also, and even more familiarly 
taken in a sense, in which it denotes oaly substances. But substances are 
not all that exist; attributes, if such things are to be spoken of, must be said 

*to exist: feelings also exist. Yet when -we speak of an" object, or of a thing, 
we are almost always supposed to mean a substance. There seems to be a 
kind of contradiction in using such an expression as that one thing is mere- 
ly the attribute of another Jhing." From this, it seems 'that Mr. Mill's defi- 
nitions of concrete and abstract names ought to have read: a concrete name 
is a name which stands for a substance ; an abstract name is a name, which 
standi for an attribute of » substance: for, otherwise, if both substances and 
attributes are to be called things, then a concrete name, according to Mr, 
Mill, covers these and leaves abstract names without an object to light upcn. 
But Mr. Mill would scarcely agree to this change of words in his sentences; 
for, he tells us that, ''White also is the name of a thing, or rather of things." 
Mr. Mill, we presume would not go so far as to call white a substance, but 
would connsider it rather as an attribute of a substance. Yet in the next 
sentence he tells us that, "Whiteness, again, is the name of a quality or at- 
tribute of those things" (whites). That whiteness is the attribute of white 
is certainly strange enough. But he would probably say that, whiteness is 
not the attribute of white, but of white things; for on the next page follow- 
ing the former he tells us, "When we say snow is white, milk is white, linen 
is white, we do not mean to be understood that snow, or linen, or milk 1s a 



45 

color. We mean that they are things having the color" (white is their attri- 
bute). "The reverse is the case with the word whiteness; what we affirm to 
be whiteness is not snow, but the color of snow T ." Well, whiteness then is 
the name of the color of snow, but such being the case w T hat is white the 
name of when we say snow is white? It may be answered that white is 
the name of snow itself and of all white things, as Mr. Mill has said pre- 
viously.. Weil then, if such be the case, what is snow the name of? Mr. 
Mill's language is merely a j argon. | But Mr. Mill proceeds to divide names 
into connotive and non-connotive, and this division he considers of the most 
importance, u And one of those which go deepest into the nature of language." 
U A non-connative term is one which signifies a subject only, or an attribute 
only. A connotative term, is one which denotes a subject and implies an 
attribute. By a subject is here meant, anything which possesses attributes. 
Thus John, London, England, are nanfes which signify a subject only. None 
of these names, therefore, are connotative. But white, long, virtuous, are 
connotative. Th3 word white denotes all white things, as snow, paper, the 
foam of the sea, etc , and implies, or as it was termed by the schoolmen, con- 
notes the attribute w 7 hiteness. The word white is not predicated of the attri- 
bute, but of the subjects, snow, etc.; but when we predicate it of them, we 
imply, or connote that the attribute whiteness belongs to them." Now in 
the above sentences, the misconception of the meaning of propositions first 
spoken of by us, is commingled with the confusion respecting concrete and 
abstract names, which we noticed a moment ago. We do not wish to fill our 
book with strictures upon the works of others, which is apt to be regarded 
at best as sensorious. The best way to cure errors is to bring forward the 
truth and let it be examined. And we repeat the remark that all the divis- 
ions of names, after that they have been divided into names of homon, 
hetera, similia, differentia, commensura and incommensura, are of but small 
importance for the purposes of explaining the reasoning processes. These 
six classes lie at the foundation and are used in assisting the undestanding in 
drawing its conclusions; the other classes are useful, if useful at all, merely 
for the purposes of distinctions in mentioning things, but they do not assist, 
but lather impede, the progress of science. 

CHAPTER IX. 

CLASSIFICATION of propositions. 
In the previous chapters, we endeavored to obtain .classifications of 
those objects with which we are familiar, and to treat of names used to mark 
and distinguish truths. And it must have been observed, that what former 
writers have called attributes we call existences, and when these existences 
co-exist, w r e name them gregaria. Among most logicians, and especially 
among the schoolmen, what they call attributes are said to inhere in a sub- 
stance. But of this substance in which attributes inhere, w T e have not been 
able to gain any knowledge whatever independent of the attributes. And we 
regard the name attribute as calculated to mislead, and therefore we do not 
it at all. And a substance stripped of gregaria is unknown to us; independ- 
ent of the capacial gregaria, we know nothing of the ego, or of any mind ; 
and stripped of facial and capacial gregaria, we know^ nothing of matter. 
And the gregaria, of which weknow something directly, may with as much 



46 

propriety at least be called existences, as those things which our thoughts, 
1'rom oUr knowledge of gregaria, lead us to suppose to be in some manner, 
we know not how, the causes between the ego and non-ego, of those gre- 
garia. We are able to say with confidence that one thing per se can not be. a 
cause, i. e , no change or effect can come out of it. We are able to say with 
e^ual confidence that red, white, sweet, etc., have not always been to us- exist- 
ences, but that with us they had a beginning; and therefore we conclude 
that our mind in and of itself must be something, and that there are other 
somethings, whose relations to the mind cause these existences, which we 

" call red, sweet, etc. 

Now when men were forming language, they were endeavoring to dis- 
tinguish by the names, which they hit upon, certain truths which had come 
to their minds. But if their name's do not point out clearly to our minds, 
well defined truths, we lay them aside and endeavor to supply their places 

'with more suitable instruments. And it must appear evident to every one 
that had any person attempted to compose a treatise on logic in the infancy 
of language, in order to have succeeded in stating what is now known about 
it, he would have had to run away ahead of his generation in the knowledge 
of things, and to have invented and explained terms which have cost the 
human intellect ages of labor to furnish to us. But happily for us thelabra- 
tory of thought has been vigorously operating for many a thousand years 
before we have been called upon to enter the arena of mind. Instruments 
for stamping truths have been prepared to our hand by nations, each inde- 
pendent of the others. And although language always has been, and always 
w T ill be behind the w 7 ants of a people who push their inquiries beyond the 
already occupied fields of knowledge; yet the advance usually proceeds with 
so gradual a pace, that there is not much difficulty usually, in forming the 
language chart of the newly discovered territory. 

Now in the preceeding pages, we endeavored to show how we obtained 
and classified the truths of which we treated: we also applied the names- 
. used for distinguishing them. At the same time, therefore, that we w T ere 
tracing the processes of the mind in gaining knowledge, we were also fur- 
nishing and setting down .the signs by wdiich to distinguish the knowledge 
obtained. And if words, as it has been said, are the forts established to 
guard and keep mental acquisitions, w r e should expect a w T riter, who puts his 
truths carefully into groups for future use, to fortify them with proper terms, 
as he passed along. This we have endeavored to do as well as we were able; 
and then w r e took a view of these names or forts. We must proceed, there- 
fore, to connect those names, or forts, together and consider the results. This 
is done by the use of propositions. 

A proposition, in general, we define to be the result of the comparison 
of existences made by the mind and expressed in words; and under this 



general definition of proposition we make two classes of propositions viz: 
logical and conclusional propositions. A logical proposition is one in 
which the result of the comparison between two existences made immediately 
by the mind is expressed in words; a conclusional proposition is one in 
which the comparison between two or more existences is made immediately 
by means of a particular existence or existences and the result of the com- 
parison is expressed in words. The sun is an existence, fire burns, snow is 
white, etc., are example of the first class. In each of these propositions there 
is a mental comparison immediately made, between two existences, and the 
result of the comparison is expressed in words.- The expressions; the sun is 
and the sun is* an existence, are equivalent: fire burns, is equivalent to fire is 
the cause of burninjr sensations: fire itself is the effect of chemical affinities. 
And hence every proposition fully stated requires a subject and predicate, 
i. e., a name to distinguish the truth upon which the mind first looks, and 
also a name to point out the truth, connected with the first in comparison. 
The comparison may frequently, by a mode of speech, be expressed by using 
the name of the subject only with a verb: and in such cases the other exis- 
tence compared is suggested and compared by the verb, i. e., the verb both 
points out aod compares the predicate with the subject. This is generally 
the case, wdien the subject or first existence considered is the reputed cause 
of the second one: as fire burns, ice cools, the sun shines, the mind thinks, 
etc. This is also the case when the first existence is looked upon as the sub- 
ject upon which some effect is produced: as beauty fades, water runs, leaves 
fall, etc. But all such propositions may be made by wording them differ- . 
ently to set. out a subject, a predicate and a copula, i. e., in each of whicji 
propositions, two well defined truths shall appear, the one as subject and the 
other as predicate, with a copula to express the result of the comparison. 
The verb used in our language, as the copula, may always be made to.be 
some part of the substantive verb to be; as snow is white. 

Now respecting the meaning of this copula in propositions there has 
been much dispute among authors. When we say that the sun is, w 7 e mean 
that the sun exists, is an existence. Ihis, indeed, is the primary meaning of 
the verb to be. But besides this meaning authors tell us that it has another; 
as when we say John is a man ; they tell us w^e use the copula is merely as 
the sign of predication. And although in the proposition, the sun is, they 
tell us is is a predicate of itself, yet when a name is placed after it, it then 
passes its predicable quality over to that name. All this is certainly some- 
what obscure. For, when we take from the verb to be its primary significa- 
tion and call it a sign of predication, wiiat do w r e mean by this expression? 
"We mean, say our authors, that the copula affirms one thing of another. But 
I do ootr see that any more light has been thrown upon the subject by the 
change ef phraseology. When we say that ice is frozen water, according to 



48 
this explanation, we affirm frozen water of ice, when in truth frozen water 
and ice are the same thing, and therefore, in truth, we affirm itself of the 
subject. But if it be explained by saying that the copula shows that the 
subject possesses the predicate, or that the predicate belongs to the subject, 
as it is usually done, we answer that this explanation explains nothing. 
For, according to this dpctrine, ice possesses frozen water, or frozen water 
belongs to ice — a mere jagon of words. But it is said "That the employ- 
ment of it (the copula) as a copula does not necessarily include the affirma- 
tion of existence appears from such a proposition as this, 'A centaur is a 
fiction of the poets,' w T 4iere it can not possibly be implied that a centaur 
exists, since the proposition itself expressly asserts, that the thing has no 
real existence." — J. Stuart Mill. To this we answer, that a centaur has a real 
existence, nor does the proposition assert the contrary. Its existence, how- 
ever, is grounded in the ego, as the proposition asserts, "A fiction of the 
poets." Although modern logicians have arrived at more certain conclusions, 
in very many respects, yet in their expositions of propositions, they are as 
much at fault as the ancients. The truth is that the verb to be as the copula 
in propositions, maintains its primitive meaning in every instance, nor can it 
be shown to have any other in any case. We may, indeed, say that it is 
merely the sign of predication, but when w r e come to examine closely this 
expression, we will find it to be merely words without knowledge. Such 
expressions as these, snow is white, John is a man, leaves are green, etc. > 
were brought into use before philosophy had made a beginning; they are 
natural, short and convenient modes of expression and explicit enough for 
the wants of mankind in communicating thought in a' general manner; the 
philosophic interpretation of them, however, by WTiters upon logic, we re- 
gard as erroneous. But we must defer the further consideration of the copula 
until we come to the interpretation of propositions, when we hope to give a 
full and clear explaination of the whole matter; and we have merely advert- 
ed to the subject here, for the sake of order, and to put the reader on his 
guard against what we consider errors. 

From the supposition that in all proppsitions there is something 
affirmed of the subject in certain cases, and something denied of the sub- 
ject in other cases, writers have classified propositions into affirmative and 
negative. But this classification, in our view, is unscientific and built upon 
a sandy foundation. Every proposition, indeed, expresses a discourse of the 
mind, which may be denied or contradicted. But if we place before our 
mind a single existence either simple or aggregate, red for instance, as the 
subject of every proposition must be, we can deny nothing of that existence: 
if we say anything at all about it, we must make an affirmation. Take the 
two propositions, John is well, a^nd, John is not well : and if we consider the 
one as a reply to the other, there will, indeed, be a denial ; but contemplating 



49 

either one of them as independent of the other, and it contains an affirma- 
tion. And further, if this appear obscure, we may ask ourselves, whether 
both expressions are really propositions, and if they are, then they must have 
something in common: proposition must be the genus of which each is a 
species. If they be differentia, and yet in some generalization similia, they 
must have been differentiated from the higher class in which they were 
similia. But if we say that the one affirms something of something, and the 
other denies something of something, as is done, they then have nothing in 
common, excepting that each has a subject and a predicate, i. e., one existence 
before and another after the copula. But if the names of the two existences 
compared in propositions be set down, as may always be done, and we dis- 
tinguish the one from the other by calling the one the subject and the other 
the predicate, this is merely a classification of the terms, and terms alone do 
make a p/oposition. The classification of terms, therefore, can not be the 
thing in common, which unites all propositions in a common class. But if 
some propositions affirm and others deny, these things (affirmation and de- 
nial) are diflerentia, and there is nothing left in which the propositions can 
agree excepting the classification of terms. In the two propositions "A pear 
is a fruit," and, "An apple is not a pear," we consider that there is no denial 
in either case, both are affirmations; though this doctrine will, no doubt, 
sound strange to those indoctrinated from the books upon logic. They 
affirm, however, results which inter se are differentia. This doctrine will be 
easily understood after that we have treated of the interpretation of propo- 
sitions. 

What we consider, therefore, the proper mode of classifying proposi- 
tions is by the differentiating of the results affirmed. We defined a logical 
proposition to be the result of a comparison made immediately by the mind 
between two existences expressed, or affirmed, in words. Affirmation, we 
consider, is the very thing in common in all propositions; but the results 
affirmed are differentia. And these results, we find, may be discriminated 
into six classes, and therefore, we make six classes of propositions, viz : 
homonical, heterical, similical, differential, commensural and incommensural 
propositions. It is not necessary that we should take up each of these classes 
and give them further attention here; for we are only classifying preparatory 
to a thorough investigation hereafter. Some^ things have to be merely stated 
at first, so that the explanation when it comes; may be understood. 

• Now each of the above classes might, apparently, be subclassified into 
simple and complex propositions. A simple proposition, then, would be one 
in which one subject is compared with one predicate, as "John is a boy." 
And a complex proposition would be one in which -one and the same subject 
is compared with each of two or more predicates ; or in which one and the 
same predicate is compared with each of two or more subjects; or in which 



50 
two or more subjects are compared Willi two or more predicates. What, bow 
ever, is called a complex proposition is really a single proposition expressed 
and one or more others understood, as "John is -good and wise," equivalent 
to "John is good and John is wise." Again, "John and James are good and 
wise," is equivalent to "John is good and John is wise and James is good and 
James is wise." "John is not good," is a simple proposition of a different 
kind, and "John is neither good nor wise," is a complex proposition of the 
same kind. And "All the Apostles were Jews," "xlll the boys in the house 
are barefooted," etc., are complex propositions. The classification of propo- 
sitions into simple and complex, however, is not a classification of propo- 
sitions, as such, but rather a division of them according to the number of 
propositions expressed and employed in a set of words which contain but 
one verb. 

But again, propositions have been divided into pure and modal, as 
"Brutus killed Csesar," (pure) and "Brutus killed Caesar justly"* (a modal 
proposition). This division of propositions is made merely from the appear- 
ance given to propositions by the warding of them, and it is not a division 
of propositions, as such, at all. The sentence "Brutus killed Caesar justly," 
contains a result which will be exactly expressed by another set of words, as 
"The killing of. Caesar by Brutus was just"; a pure proposition. The divis- 
ion has no foundation, whatever, in the nature of propositions, but rests en- 
tirely upon the wording of them. 

But again, propositions -have been divided into universal or general, as 
"All men are mortal"; particular, "John is mortal"; individual or singular, 
"A man is mortal"; and indefinite, "Some men are strong". We, however, 
reject these divisions, as divisions of propositions, as such. The w r ords all, 
every, some, etc., joined to subjects or predicates qualify them and make 
them a certain kind of subjects and predicates, but the affirmations is made in 
such propositions, just as it is, where these w T orcls are wanting. These w T ords, 
therefore, qualify the results of comparisons only by their qualifying effect 
upon the existences compared in propositions, the manner- of making the 
affirmation is in no way affected by them; they belong to subjects and predi- 
cates and not to the result affirmed wiiich is the essence of propositions. 

The sub-classification therefore, which we will make, is into categori- 
cal and hypothetical propositions. A categorical proposition is one in which 
a certain result is expressed as-actualiy existing in the relation of existences, 
as red is a color, red is not green, etc. An hypothetical proposition is one 
in which a certain result is/supPosED to exist in the relation of existences, 
for the purpose of drawing some conclusion from it; as "If a sheep be a 
horse, (hypothetical) a lamb is a colt" (conclusion). This whole phrase 
would be considered 'hypothetical by writers upon logic. The hypothesis, 
however, lies in the first proposition, "If a sheep be a horse," the latter sen- 









51 

tence is not hypothetical, but a categorical conclusion, which expresses a 
result flowing actually from the hypothesis; but the hypothesis being false 
the conclusion depending upon it must be false also. 

Now before leaving logical propositions, we must say a few things 
about subjects and predicates. Subjects may be divided into simpje and 
aggregate. A simple subject is a single existence per se, as "Red is not 
gseen," here red is a simple primary propositional truth. An aggregate sub- 
ject is an aggregate existence, as "Iron is hard." Here iron is an aggregate 
existence made up of certain facial and capacial greparia entering into a 
kind of fasciculus, which gregaria are the things in fasciculo for which the 
subjective term stands and which it distinguishes. Predicates are divided in 
like manner. This is all that we need»say at present respecting subjects and 
predicates: when we come to unravel the meanings of propositions, we will 
have to consider subjects and predicates more fully. And this brings us to 
notice logical conclusions, or conclusional propositions, about which we will 
say but little at present as they will be treated again hereafter. 

A logical or ratiocinitive conclusion, as alread3 r said, is a proposition 
in which the result of comparisons mediately made by means of certain ex- 
istences, is expressed in words. In a logical proposition the result of the 
comparison made immediately between two existences is expressed in words ; 
but in a conclusional proposition the result is not derivec^from the immediate 
comparison of two existences, but mediately, as A is equal to B, C is equal to 
A, and therefore C is equal to B (a conclusion). In the last proposition, 
which is a conclusion, the comparison between C and B is not immediate, but 
mediate by the means of A. This distinction between logical propositions 
and conclusional propositions is important to the clear understanding of 
logic: for it is evident that a conclusion once gained may be made the 
premise in a subsequent S3'llogism, and unless we understand this distinction, 
we will not know how to get to the bottom of the reasoning process. 

All those propositions which have been denominated modal, by writers, 
are conclusional propositions, as "Brutus killed Caesar- justly" is a conclusion. 
And much of what we have already said about logical propositions, will 
apply to conclusional propositions, we need not therefore, repeat it. Propo- 
sitions, which are called disjunctive, al c o, are not logical propositions proper, 
but conclusions, the premises of which are often not mentioned: as "John is 
either a knave or a fool," is not properly a logical proposition, but a conclu- 
sion drawn from some premises, which are found in and can be made out of 
John's actions. What have been called hypothetico disjunctive or dilematic 
propositions, also, are conclusions, as we will more fully see and explain 
hereafter. 

In this chapter we have endeavored to classify propositions so that we 
may be more easily understood in our subsequent inquiries. All truths, and 



52 

especially those about logic, are so interlinked that we are obliged to draw, 
sometimes, upon those whose explanation has not yet been .given in order to 
accomplish the work on hand. And the subject upon which we have been 
engaged and which we must yet consider more closely, has been misunder- 
stood, as we believe, by all writers heretofore upon logic. 

CHAPTER X. 

HOMONICAL PROPOSITIONS. 

We have denned a logical proposition to be the result of a comparison 
between two existences made immediately by the mind and expressed in 
words : and a conclusional proposition to be the result of comparisons be- 
tween existences made mediately and expressed in words. We will first give 
our attention to logical propositions. And the result expressed in every logi- 
cal proposition will be either a truth or an error. If our faculties be in a 
perfect state and exercised i'n the right manner, the result will generally be a 
truth: but if our faculties do not act in a legitimate and sufficiently vigorous 
manner, we will obtain an error. In every instance, therefore, it is always 
necessary, in order to obtain a truth by comparison, that we should have an 
adequate knowledge of each of the two truths compared in logical proposi- 
tions. We have already shown that all existences may be compared one with 
another, and that Wiowledge is a result brought out of the relations of exis- 
tences. To show, indeed, how the mind possesses the capacity in itself to 
compare is no part of our undertaking; but that it actually does compare 
among the existences which are the subjects of its cognitions, and hence 
gain knowledge by the comparisons, we think, has been sufficiently shown 
already. 

Now when the mind has gained knowledge and clothed this knowledge 
with words, i. e., given it as it were, a body to render it visible to others, the 
knowledge gained, indeed, is thus made appreciable to others, but the opera- 
tions of the mind in gaining that knowledge, leave no trace behind. And 
did every proposition' clearly exhibit the two existences compared, and also 
the result or truth gained by their comparison, propositions would need no 
interpretation, for each one would fully interpret itself. But the men who 
commenced language, were seeking merely for an instrument of utility in 
the common affairs of their lives, in which clearness of detail and precision 
of expression were of less importance than general availability and dispatch. 
And therefore, in every language, the truths which are really compared in 
propositions are sometimes but dimly shadowed forth, and the result of their 
comparison always but obscurely shown by the form of the words. And this 
makes it necessary, in order to obtain a thorough insight into propositions, 
to show what the two truths compared really are, that the result of their com- 
parison may be clearly perceived. To this task, therefore, we now proceed; 



53 

and we will commence with the examination of homonical propositions. 

Take the proposition "Red is red," and let us endeavor to clearly set 
out the two things compared and the truth, which is the result of their com- 
parison. And first, we must observe that an existence which is absolutely 
the same existence can not be two existences, and that one thing per se can 
not be compared at all : two existences. must always be found in every propo- 
sition. We must al so- observe that when we have the knowledge of an exis- 
tence, we can always make some discrimination respecting that existence: for 
wiihout some discrimination we can have no knowledge. Plurality of ex- 
istences is necessary to our knowledge of any one; and, therefore, absolute 
oneness or identity is not within our knowiedge: every truth of which we 
have any knowledge is evolved from relations. But how then can we say 
that "John is John," or what is equivalent to this, "John is himself"? In 
order to understand this it is necessary to recollect that some truths are 
grounded in the non-ego and others in the ego. If we look at a tree, the relations 
between the tree and the ego bring to our knowledge an existence (a tree) 
grounded* in the non-ego, and also an internal existence grounded in the ego. 
Now simple existences'can only be discriminated by their wheres, by their 
times and by their effects. Many effects upon the mind are inter se similia; 
thus if we look at an inkstand to-day, and to-morrow look at it again ; both 
to-day and to morrow it will produce effects upon the mind exactly similar: 
yeWhese effects will not be the same, they will not be homon, for they can be 
discriminated by their times. But similar effects upon our minds can only 
be discriminated by their times: and where there can- be no heteration of 
times made, there can be but one and the same existence grounded in the 
ego, # similarity is lost in identity. And we must always recollect that by the 
ego, we mean my mind for me and your mind for you. For should I and a 
thousand other persons, at one and at the same instant ot time, look at an 
object and be affected by it exactly alike, yet to me only one of these effects 
would be grounded in the ego : and all the effects upon the minds of the 
others in respect to myselt would be grounded in the non-ego. Similar 
truths, therefore, grounded in the ego, which can not be differentiated, but 
whose times can be heterated, are not one and the same, but separate exist- 
ences: they are hetera. But with respect to truths grounded in the non-ego, 
though their effects upon the mind may be exactly similar, or to change the 
form of expression, these truths may exactly resemble each other, yet if their 
wheres can be heterated, they are not the same but separate existences. If 
three men receive mental impressions exactly similar, yet any person can 
heterate the wheres of these effects and therefore the effects are not the same. 
Dissimilar truths grounded in the non-ego, or in the ego, can be discrimi- 
nated into differentia, they can be differentiated ; but similar truths grounded 
• in the non-ego, whose wheres can not be heterated, are to us the same. If 



KA 

ode « 

we should see a rock of a particular shape and color to-day in one place, and 
to-morrow see a rock exactly similar in another place, the only thing which 
would enable us to know that these two rocks are not the same, is that their 
present wheres are hetera. If we should find out that the first rock was no 
longer in.its wonted place, and we could not tell the where in which it now 
is, we would most likely conclude the second one to be it. BespectiDg simi- 
lar truths grounded in the ago, therefore, the heteration of their times alone 
destro}^ the identity : respecting ^similar truths grounded in the non-ego, 
time being the same, the heteration of their wheres destroys the identity-. 
The power of the mind to heterate depends upon the time and spxicc. . 

And now we look at John and receive .a mental effect, and again look 
at him and receive a similar effect, the times of these effects can be heterated, 
and hence there are two similar existences grounded in the ego, which can 
be compared with each other, But if we project these existences and ground 
them in the non-ego, at the very time we last- looked at John, we knew of but 
one where for these two subjective existences to exist objectively, and hence 
no heteration, objectively, of their wheres can be made; and, therefore, as 
they are subjectively similia, they are objectively to*us. homon: and hence 
we can say that John is John, or that John is himself. The mind can pIso 
gain a truth grounded in the non-ego and afterwards recall it by what we 
call memory: and as often as the mind does thus recall one and the same 
objective truth, so many subjective truths inter se similia, but not 'identical, 
will pass through the ego, any two of wjiich may be compared and projected. 
And respecting the projection of truths from the ground of the ego into that 
of the non-ego, we have already seen heretofore, how existences are divided 
by the mind into those grounded in the ego $nd those grounded in the non- 
ego. 

And hence*the meaning cf the proposition "John is himself," is that 
John, grounded in the non-ego, and himself, grounded in the non-ego are 
the same thing; John and John who are subjectively hetera are objectively 
homon. We may say that John and himself are the same thing, or that John 
and himself exist identically, or that John exists as himself: whatever may 
be the words and their syntactical relations, the two subjective existences, 
each of which we call John, are objectively the same, and what is affirmed 
by the proposition, is homon. None of these expressions, however, mark in 
words with entire fullness the whole of the mind's operations, but merely 
state or set down the existences compared and affirm the result of the com- 
parison. And in a large class of propositions," all of that' class, which we 
have called homonical, the result of the comparison made by the mind is 
homon, homon is the thing affirmed. Thts is always the case in those propo- 
sitions which defined words, i. e., in which the meaning of a word is ex- 
plained by some synouim or equivalent expression: as faithfulness is fidelity. 



i. e., the meaning of the word faithfulness and that of fidelity are homon 
The following propositions are similar to the one first spoken of: "Sim is the 
name of the orb of -cTay;" "Death is the name of the end of life;" "Term is 
a name given to each of the names which distinguish the existences com- 
pared in a proposition;" and so on. All of these propositions are homoni- 
cal, homon is affirmed in each one-of them. 

Such propositions as the one above have been called verbal, because the 
existences compared in them are words. And according to the old but erro- 
neous sj^stem of predication, in such propositions, one name is predicated or 
affirmed of another. One name, however, cam not be affirmed of another, 
nor can one existence be affirmed of another; the only thing that can be 
affirmed, in such propositions as we are now treating of, is homon. In those 
propositions, also, which are called real, in these, which explain the nature of 
the- thing defined, homon is the tiling affirmed; as "A triangle (tire thing, 
signified by the word) is a figure, having three Sides and three angles," "The 
eye is a physical organ by which we see," "A primary property of matter is 
impenetrability," and so on. 

..But in the proposition "John is John," which we considered a little 
while ago, we notice that both the subject and predicate are aggregate exis- 
tences, and that each one is compared with the other in the aggregate as a 
totality. JSTow when the subject is an. aggregate existence,' and it is viewed as 
a totality, and all of its gregaria are taken collectively, the predicate must 
also be compared in the aggregate in ail homonical propositions: for an 
aggregate existence, as a totality, can. not be the same as a simple existence, 
a gregarium, and vice versa. But there are homonical propositions in which 
the subject, in appearance, would seem to be an aggregate existence viewed 
as a totality, "while the predicate is very plainly a simple existence, a gre- 
garium : we "must therefore examine such propositions. 

We must always keep in view that im every simple proposition, two 
existences and only two are compared: in logical propositions these two ex- 
istences are immediately compared, and in conclusional propositions they 
are mediately compared. These two existences may be, each of them, sim- 
ple, aggregate', or collective ; yet there can but two enter into the comparison 
in the' proposition of which the result is expressed in words.: And one of the 
difficulties in tjic way of understanding propositions, is to ascertain what are 
really the two existences and the nature of each of them in the proposition. 
This difficulty .has not been overcome by any writer upon logic, heretofore, 
with whose work we are ac*quainted.f . 

Mow when we say that Snow is white, or that Iron is fusible, we 
might believe that snow and iron, aggregate existences, are compared in to- 
tality, with 'their predicates respectively: this however, would be entirely 
erroneous. And in order to ascertain and clearly exhibit by the wording of 



50 

the proposition, the two things which are really compared, we have to state 
the proposition thus; One of the capacifl gregaria of iron is fusibility, a 
proposition in which a like result is obtained as in the other, and in which 
two simple existences, which are the things really compared distinctly appear. 
And if the proposition be stated so that the homonieal nature of it also shall 
clearly appear, it will read thus; One of the capacial gregaria of iron and 
fusibility are homon. And in all homonieal propositions in which the sub- 
ject is ;m aggregate existane.e aud the predicate I simple one, it is only one of 
the gregaria of the aggregate existence, that is compared. In the proposi- 
tion, Cataline was ambitious, when the tilings actually compared are 
clearly set out it will read Ono of the capacial gregaria of Cataline was am- 
bition, i. e., one of the capacial gregaria of Cataline and ambition are 
homon. When we say lied is rod, the result oi the comparison is easily 
seen, because we plainly see that both subject and predicate are simple exis- 
tences; but when the real subject is covered up by a term which signifies an 
aggregate existence, and the predicate is simple, we are misled. 

And hence in such prepositions as Iron is fusible, writers have said 
that the predicate is affirmed of the subject, or that the predicate is contained 
in the subject and so on, all of which expressions not only give erroneous 
notions of the nature of propositions in general, but per se they are utterly 
false: for the existence which pw>positionalJy is called the predicate is com- 
pared with the subject and the result of such comparison is what is affirmed 
in every proposition. And although fusibility is one of the capacial gregaria 
oi' iron, and it is contained in this aggregate existence, yet this aggregate ex- 
istence in totality is not the subject of the proposition Iron is fusible, but 
this capacial gregarium of iron is the subject. We have already shown that 
in every proposition two subjective existences, i. e., existences grounded in 
in (he ego are compared: and in the proposition Iron is fusible, two fusi- 
bilities are sujectively compared, and subjectively they are similia: and then 
they are objectively located as homon in the aggregate existence iron, and 
this is the result of the comparison in the proposition Iron is fusible. 

Now T as there are but two classes of subjects, simple and aggregate, 
and so also 01 predicates, it would not oe necessary at present to say any- 
thing farther respecting homonieal propositions were, there not sometimes 
set down the wards all, evt rv, most, some, the whole of, none, both, etc., 
alonig with subjects and predicates: but homonieal propositions in which 
these words are either expressed or understood need a further investigation. 
And when we say that All iron is,fufible, which writers have called a uni- 
versal proposition, what dower mean by the words Am, iron? As iron is 
an aggregate existence, let us first examine a simpler case; take the proposi- 
tion All red is red, i. e., red and red are homon. Now almost any one will 
say that this proposition is self-evident, because were the predicate anything 



57 
else than red, it could not objectively be the same thing as the subject, which 
is red. Now this explaination can easily bo applied to unravel the mysteries 
oi the proposition All iron is fusible. For this proposition may be thus 
stated, One of the capacial gregarium of all iron and fusibility are homon. 
And front this proposition, it must appear, that were fusibility lacking in an 
aggregate existence, that existence could not be iron. Fusibility is a neces- 
sary gregarium in any aggregate existence, which we distinguish by the 
name, iron; and consequently it must exist in this piece, that piece, and in 
all pieces of similar aggregations. 

The word all standing before iron does not indicate that the mind 
must have made what is usually called an induction, i. e., that the mind from 
a great number of instances has determined the laws of nature to be uniform, 
and therefore this p\ece and that piece will fuse. The discovery of the capa- 
cial gregarium, fusibility, in one single piece of iron, if by this gregarium 
we distinguish an aggregate existence from others, and mark the distinction 
by the word iron, will enable us to say with certainty and truth that All iron 
is fusible ; for in c\oing so, we merely state that one of the necessary gre- 
garia of an aggregate existence, which we distinguish by the name iron, and 
fusibility are homon. That there may be other gregaria in the aggregation, 
of which as yet we know nothing, does not change the case at all. 

Suppose a person to be taken into a large room in which there were 
four kinds of balls upon different shelves around the apartment, and he be 
required to give distinguishing names, which would enable him to speak 
afterwards about the balls, respecting merely their tastes and colors. He 
would take up the first one at hand, and perceive that it was of a red color 
and had a sweet taste, and therefore he would name this ball A. Then every 
ball in the room that was red and sweet, as balls of colors and tastes, which 
are inter se similia, can not be differentiated, must be called A from a men- 
tal necessity. And by the name A, they are afterwards distinguished from 
those ih at are blue and sour, which might be called B, and from those which 
are white and oitter, which might be called C, and so on. But so soon as he 
had given the name A to distinguish the first ball of a red color and sweet 
taste from others, all balls of a red color and sweet taste must be called A, 
and if so, could he not immediately after naming the first ball, 
have said with perfect certainty and truth that all A is red and all A i» sweet? 
And it afterwards, a red ball should be found that was sour, it would not be 
an A, but it must be called by some other name. 

But an Indian, before the discovery of America, might have said that 
all men are red, for he had never seen any man of a different color, yet his 
assertion would not hav£ been true. The ancients also, might have said and 
cyd say, that all swans are white, yet such is not the case. And the error in 
both these cases lies in taking-the gregarium of a particular object or objects 



58 
and making this gregarium in our mind, one of the necessary gregaria to dis- 
tinguish this object from others, when it is not so: there were other things 
red besides Indians, and other things white besides swan's, when animals 
were distinguished by names : the color was not one of the gregaria by 
which these objects were necessarily distinguished. 

But we hare said that aggregate existences are distinguished Inter se 
by the facial and capacial gregaria co-existifig. And hence did one aggre- 
gate existence contain similar facial but not similar capacial gregaria with 
another, the two aggregations would not be similia, and they could not be in- 
telligently distinguished by the same name. A distinguishing name, is a 
word taken at pleasure to distinguish existences inter se; and r *when it stands 
for an aggregation, any oae of the gregaria sine qua non, can not be lacking, 
and the aggregation be called by the same name as a« object in which it 
exists. Charcoal and the diamond are said to be, as elements, similia, yet the 
gregaria differ and consequently we can not speak of each intelligently and 

use the same name. 
Mi 
But how then, say you, is it that a- black swan and a white one may 

both be called swans ? Simply because they are differentiated inta swan's 
irrespective of their colors, just as red and w T liite, as we have seen, are first 
differentiated into color, and then distinguished inter se, by the names red 
and white. 'All men are mortal, is a proposition of the same kind as All iron 
is fusible. Mortality is one of the capacial gregaria sine qua non of man, 
and a living being not subject to death would not be a man. The proposi- 
tion, All men are mortal, however is a very different one from, All men are 
mortals; the first affirms homon of mortality and one of the capacial gre- 
garia sine qua non of man; the second affirms man and one of the aggregate 
existences called mortals to be homon. All men are animals, and, All sheep 
are animals, are similar propositions, and they may be thus interpreted: man 
and one species of animals are homon, sheep and one species of animals are 
homon. 

But to pursue further the effect of the word all in propositions, if 
when man 'was first placed upon the earth, he had 'lived to the age of ten 
thousand years without a death occurring, and if during that period he had 
invented language and distinguished himself by the name man, it is plain 
that nfortality would not have been in his miftd one of the capacial gre- 
garia of himself: 1 he would not at least have known this by direct observa- 
tion. And if during this time, no'constituttonal changes among external 
objects had come to his knowledge, it is evident that he would have known 
nothing at all about the capacial gregaria of objects; but all the names in 
his language would have been signs to distinguish simple existences inter se, 
and aggregations of facial gregaria. And therefore all the aggregate exis- 
tences now classified by their capacial gregaria and marked by distinguish- 



59 

ing names, would have remained unclassified. And then each one of the 
facial gregaria, which„was a sine qua non of any class, would have been a 
necessity in order that any object might have been called by the name given 
to individuals of the. class. Names, of course, under the circumstances 
would have been few in number. But suppose now, that at thcencl of the 
period v above spoken of, one of the human species had died, here would have 
been to mankind a new truth learned by observation. And were this instance 
of death then made known to all the living, all subsequent deaths would not 
have been new truths, but other instances of similar truths. And although 
non simile est idem or non similia sunt idem, objective^, yet subjectively 
similia are the same thing if time be left out of the question. And hence 
respecting the knowledge of truths in the mind, the recurrence of similia are 
regarded and often spoken of as other instances of the same truth, although 
they are not homon but similia; their times arehetera and therefore the truths 
are similia, but were their times homon, the truths also, would be subjectively 
homon. Now if we have gained the knowledge of one individual of similia, 
we have gained all the knowledge we will ever have of the similia, except- 
ing their number or instances. And therefore after one death had occurred, 
the question would have been, men being similia in those gregaria which to- 
gether make the object distinguished by the name 4 man, is death one of these 
capacial. gregaria? That it is could have been proved to men under the 
above circumstances only by a process of reasoning which we shall develop 
hereafter. (See book 1, chapt. xxii.) But so soon* as it is established to" be 
such, it is a sine qua non of man and hence we say that death and one of the 
capacial gregaria of all- men are homon. And as aggregate existences are 
composed of certain facial and capacial gregaria, which are the very things 
which distinguish trrem into classes of similia, when any one of these gre- 
garia sine qua non is known and given a name, it may be made the predicate 
of an homonical proposition, in which the word all names the sum totum of 
the aggregate existences for any one of which the noun placed after all 
stands as the name. And hence that all iron is fusible, when fusibility is once 
in our minds a sine qua non of iron, is a necesshy of our minds. It may be said 
that fusibility is not a gregarium sine qua non to distinguish iron from other 
things; for gold and other metals possess it. This is true; but go one step 
back into the class of things called by (lie name metal, and we will find fusi- 
bility to be one of the distinguishing gregaria, and in subclassifications this 
gregarium must pass into each of the subclasses; for they, each of them, 
under the name metal possessed it. And hence by adding the words all 
and every to the name of an aggregate existence and then making the term 
the subjective one of an homonical proposition with a simple existence as 
the predicate, we show this simple existence named in the predicate to be one 
of the gregaria sine qua non of the aggregate existence named in the subject. 



60 

All gold is proof against the effect of nitric acid, i. e., one of the capacial 
gregaria sine qua non of g©ld, and proof against the effect of nitric acid are 
homon. 

But we must now examine the function of the word some when placed 
before the name of an aggregate existence in a proposition* Take the propo- 
sition Some ink is red, i. e., one of the facial gregaria of some ink and red 
are homon. Now it must appear that the facial gregarium here mentioned is 
not a sine qua non of ink, but that it is one which compared with some other 
color, enables us to differentiate inks. Some therefore, as it names the part 
of a whole, shows also by being placed before an aggregate existence in 
homonical propositions, that the gregarium, which appears as a simple exis- 
teuce in the predicate; is not a sine qua non of the class of aggregate exis- 
tences distinguished by the name which appears in the subject and named 
by the noun after some. 

We do not deem it necessary to pursue the subject of homonical 
propositions further at present. If the reader will carefully study what has 
been said already, we think he will be able to follow and understand the 
arguments, which we will advance hereafter. We will, however, set down 
several homonical propositions in the language that is uaed in common dis- 
course, and the reader can change the phraseology, so as to make the result 
affirmed appear plainly to be homon : Some men are black-eyed ; All fowls 
* a y e gg& ; All gold is maleable ; God is love ; An apple is an apple ; A straight 
line is the shortest distenCe between two points in space; Ice is frozen water; 
Schuylkill is the name of a river in Pennsylvania; Washington died at 
Mount Vernon; We are living in the nineteenth century of the Christian era; 
Columbus discovered America A. D. 1492; Shakespeare was a dramatic 
author ; Sophocles wrote JEdepus Tyrannus ; Newton discovered the univer- 
sal law of gravitation. 

CHAPTER XL 

HETERICAL PROPOSITIONS. 

Having treated of homonical propositions, we hope, with partial suc- 
cess, we come now to speak of the second class, which we hare called heter- 
cal propositions. And heterical propositions affirm results, which are 
directly the opposite of those affirmed by homonical ones, and consequently 
the two classes are differentia; and when a proposition of the one class is 
spoken with reference to the other, it denies the affirmation made by the 
other. Jf any person affirm that A is B, i. e., that A and B are homon, and 
another person rerjly that A is not B, i. e., that A and be are hetera, the latter 
makes and affirmation contradictory of the affirmation of the former and 
vice versa. 

Now if we take two twenty dollar gold pieces which are inter se 



61 

similia, and lay them before us, any person will say this piece is not that one. 
But the two pieces being inter se similia, if you hand one of them to a per- 
son, and then take it again and put the two together, and ask the person which 
one lie had in his hand, he can not tell. How then does any one know that 
this piece is not that one, i. e., that the two pieces are not homon, but hetera? 
Simply because the wiieres of the two pieces at the same time can be keterated. 
But is not the proposition, This piece is not that one, an independent propo- 
sition, i. e., a proposition expressed without reference to any other? If it is 
such, then it can not contain a denial or negation of the subject, as it is 
generally supposed, but it positivelj r affirms this piece and that piece to be 
hetera. You can not numerically count pieces of money without heterating 
them, and 3^011 can not express in words the heteration of them without using 
an heterical j/roposition or propositions. What is the difference between 
These two pieces are separate existences, and This piece is not that one; leav- 
ing the wording out of the consideration ? The difference is this, the former 
proposition never could have been put into words at all, without the latter 
one having first been menially at least enunliated: the latter proposition 
must preceed the former in the mind, or a knowledge of the tormer never 
could be gained*: in effect, however, the two are alike. The former proposi- 
tion may be resolved into This piece is an existence and that piece is an exis- 
tence and the whole expression is exquivalent to This piece is not that pie<te 
i. e., thi3 piece and that piece are hetera. And every heterical proposition may, 
in effect, be exactly expressed by the use of two homonical ones, by placing 
the distinguishing names of hetera, this and that, before their subjects: two 
homonical propositions may also be condensed into one* similical or corn- 
mensural one; or they may be differentiated or incommensurated, in differ- 
ential or incommensural propositions, as we shall see hereafter. But there 
must be an heteration of existences in the mind before any proposition what- 
ever can be expressed; for we have already shown that the process of heter- 
ation lies at the very foundation of knowledge. And this process of hetera- 
tion can not be a negative process; it must be positive or it would amount to 
nothing, and its positive character can not be expressed but by an affirma- 
tion. This has been overlooked, heretofore, by all writers upon logic. Be- 
cause the particle not is found in the proposition, it has been universally 
believed that the predicate denied something of the subject, or that the predi- 
cate was denied of the subject; a proposition, which follows legitimately 
enough from an other, which is that when this particle is omitted, something 
is affirmed of the subject, but boih of these suppositions are untrue. The 
predicate is no more affirmed or denied of the subject in^ propositions than 
the subject is of the predicate; the two existences are compared, the one 
with the other, and that which is affirmed, in all cases, is the result of the 
comparison. It rs impossible for the human mind to affirm or deny one 



62 

existance of another; all that we can do is to affirm some relation existing 
between existences. 

One and the same existence of the non-ego can not sustain heterical, 
similical or differential relation to the ego in an homonical time; for if it 
could, we could have no knowledge of identity. When we say, therefore, 
that A is not B, we do not mean that A does not exist, or that B does not 
exist, fur both must have an existence grounded in the ego at least, or we 
could not put their separate names down on paper; but, by A is not B, we 
mean that A and B exist heterically, that A and B are hetera. The particle 
not, therefore, in propositions, stands as the sign of heteration made by the 
mind, but the result of the heteration is positive, and it is affirmed in all 
propositions containing this particle. And we lay down this rule: That 
whenever the wheres of existences grounded in the non-ego can be heterated 
in an liomonical time, and whenever the times of existences grounded in the 
ego can be heterated, the heterical relations of tjiese existences are expressed 
in heterical propositions. 

In homonical propositions we saw that the wheres of the two existences 
compared, could not at the same time be heterated. When we say, John is 
John, the subject and predicate subjectively have the same where, but not an 
homonical time: John and John objectively have the same whereat the same 
time, and therefore, objectively they are homoh. But the objective John and 
the subjective John are hetera because their wheres at the same time can be 
heterated; and John and John are subjectively hetera because, though their 
wheres are homon, they can not have an homonical time. And, therefore, 
homonical and heterical propositions contradict each other, when their sub- 
jects are similia in every respect, and their predicates similia leaving the 
particle not out of the consideration. 

Now in heterical propositions, we make no account of the similarity 
or dissimilarity of existences; all we care about, is to be able to heterate the 
wheres of existences grounded in the non-ego at any given time, and the 
times of existences grounded in the ego, and then we affirm hetera. And 
hence if we place two white marbles before us, the color of the one and that 
of the other being perfectly similia, yet we say that the color of the one is not 
that of the other, i. e., the color of the one and that of the other are hetera; 
for the wheres of these colors can be heterated. When, however, we look at 
a (one) marble and say The color of this marble is white, or to use the short 
expression, This marble is white; the color of the marble and white sub- 
jectively have the same where, but heterical times; but when we project these 
subjectively heterical colors which are inter se similia, into the objective 
marble, they both have the same where at the same time and therefore, we 
affirm homon. 

Now we have, heretofore, divided subjects and predicates into two 



63 

classes, simple and aggregate. And of simple existences, some become the 
gregaria of aggregations, others do not. Time and space are never gregaria. 
And we must have observed that it is the relations of simple existences or of 
aggregations in time and space, that enable us to affirm homon or hetera; 
the power of the mind to heterate depends upon time and space. When we 
say that this apple is not that one, we apparently compare one apple with the 
other immediately: the existences, however, which are immediately com- 
pared, are the wheres of the one and the other at the same time. But when 
w r e say subjectively, An onion is not a peach, this proposition is more than 
heterical and it belongs to the differential class, which we will treat of 
hereafter. If, however, we say this peach is not that onion, we heterate the 
wheres and affirm hetera, and this is shown by the words this and that. 
And if the reader will bear in mind, that whenever he can heterate the wheres 
of existences at the same time, or subjectively heterate the times of subject- 
ive existences, the proposition may be heterical, we think he will be able to 
detect heterical propositions, whenever he may find them in books or conver 
sation, by some words which distinguish hetera. 

We will set dcw T n a few heterical propositions for practice: Philadel- 
phia is not New York; The Pacific Ocean is not the Atlantic; My hat does 
not lie on the floor; The birth-place of Washington was not Boston; This 
Land is not that one. f 

CHAPTER XII. 

BIMtLICAL PROPOSITIONS. 

When treating of homonical propositions, we showed that absolute 
identity makes no part of our knowledge; that in all homonical propositions, 
the existences compared are alw T ays subjectively hetera; that heterical results 
in the order of time always precede our knowledge of identity, and are the 
very first results obtained ; that the knowledge of the existence of any simple 
existence is dependent upon hetera; and that unless heterical results can be 
obtained, chaos reigns supreme. If I see a horse to-day and to-morrow see 
the same horse again, nevertheless, subjectivel} r , I have seen two distinct 
horses; and when viewed as existences grounded in the ego, I distinguish 
them by heterating their times, but when projected onto the ground of the 
non-ego, the heteration of their times does not distinguish them and as I can 
not heterate their wheres at the same time, I can not distinguish them at all, 
but pronounce them to be homon. 

But suppose that subjectively I consider heterical existences and can 
not further discriminate them, and objectively also I heterate the existences 
but can distinguish them no further, then we call the existences similia. And 
hence when we can heterate subjective existences, but can proceed no further, 
the existences are subjectively similia, and when we can heterate objective 



64 

existences but can distinguish theuTno further, the^existences are objectively 
similia. And, therefore, objective homon is always subjective similia, but 
not always vice versa; for subjective similia may also be objective similia. 
Subjective homon can not be expressed in a proposition, i. e., two acts, feel- 
ings or states of mind can not be one and the same, they must be hetera, and 
one thing per se can not be compared. 

Take the proposition This orange tastes like that one, i. e., the tastes 
of this one and of that one are similia. Now the sensations of the taste of 
the one and of the other, as existences grounded in the ego, are similia, and 
when projected onto the ground of the non-ego, each one is a gregarium of 
heterical objects whose wheres can be heterated, and therefore, objectively,the 
tastes are similia. We need not proceed further at present with similical 
propositions. We will subjoin a few examples for practice: This apple 
tastes like that one; John is like his father; Time is like a silent river. 

CHAPTER XIII. 

DIFFERENTIAL PROPOSITIONS. 

We proceed now to the consideration of the fourth class of proposi- 
tions, namely, differential propositions. And when two subjective existences 
can be discriminated by anything besides their times, the existences are sub- 
jectively differentia. The effect produced upon and within the mind by red 
is different in kind from the effect produced by green, and hence the two 
effects are not only hetera subjectively, but also differentia. And existences, 
which are subjectively differentia, must necessarily, if each have a corres- 
ponding objective existence, be also objectively differentia. But hovv or why 
it is that the mind is able to discriminate between red and green,subjectively, 
we do not sufficiently understand. The two objects, which produce severally 
these different effects upon our minds. Sustain in some manner different re- 
lation to the ego: they are other different elementary principles, or the one 
is composed of more or differently arranged gregaria than the other. Let 
this be as it may, for logical purposes it makes no difference to us; every 
person will distinguish subjectively and objectively red from green, and 
consider them to be things differing in kind — differentia. 

We have already stated that subjects and predicates of propositions 
are either simple or aggregate existences. And when both subject and predi- 
cate are simple existences, the differentiation clearly appears. That red is 
not green ; will easily be seen to be a differential proposition. The sign not 
does not indeed of itself indicate whether the existences have been differen- 
tiated or meiely heterated. But heteration can easily be distinguished from 
differentiation, if we look at the terms of the proposition. In the heterical 
proposition, This red is not that green; we see that the terms are particular 
names, the names of individual existences, and that the distinguishing heteri- 



heterical names, this and that are joined with the common name?, red Oiid 
green, and thus making red and green the names of particular individuals: 
While in the differential proposition Red is not green, red and green are 
unlimited common names. The name red stands for this red, that red and 
for any red, and so also with green; but when we say this red, or this or thai 
green we mean an individual. And hence in heterical propositions, the term* 
are individual names, A'hile in differential propositions, they are unlimited 
common names. And we may assert with truth that all red is not green: 
though this proposition, from the custom of our way of speaking, seems to 
imply that some red is green, and to avoid the effects of language upon our 
minds it is usual and better to say that no red is green. We are accustomed 
to say with truth that all men are not black, 1. e., one of the gregaria sine qua 
non of man is not black, i. e., black and each of the gregaria sine qua non of 
man are differentia, and therefore, by implication we affirm that some men 
are, or may, be black. And hence the custom of language, when we say that 
all red is not green, would lead us^to inter that we meant, some red is grem, 
i. e., that some red and green are homoir In every [imposition, therefore, in 
which the particle not occurs, and the subject and predicate are simple exis- 
tences, if the teims are unlimited common nomes, the proposition is differen- 
tial, it they are particular names the proposition is heterical; as John is not 
Charles. And this is also the case when both the subject and predicate are 
aggregate existences, as a man is not a horse, is U differential proposition ; 
Tins man is not that dog, heterical. When, however, the subject is an aggre- 
gate existence and the predicate a simple one. Some further explanation 
seems necessary. Take the proposition snow is not black. This proposition 
may be thus stated: Each gregarium of snow and black are differentia. No 
snow is bhick means the same thing, and guarding against the custom of 
language, we may say that all snow is not black; better — No snow is black. 
All these propositions mean the same thing. All snow is white means that 
one of the gregaria sine qua non of snow and white are homon ; but no 
snow is blaek, means that each gregarium of snow and black are differentia. 
And hence in all propositions x<> is always the sign Of differentiation. 

None is equivalent to no one, of which words it is compounded ; an 1 
when we say that none of the horses are gray we mean that no one of the 
horses is gray, i. e., gray and the color ot any one of the horses are differentia. 
No one of the horses is gray, however, is a very different proposition in its 
terms than no horse is gray, i e., each gregarium of any horse and gray are 
differentia. 

We here subjoin a few examples for practice: A river is not an ocean ; 
an Indian is not a negro; an apple is nota peach ; no fish is a bird; a gosling 
is not a chicken ; gunpowder is not saltpeter; steam is not water ; none of 
the pupils are learned; a true christian is n«t vicious; cotton is not wool; 



66 
iron is not explosive; day is not ntgbi; cause is not effect; no liorse is a stone; 
the rainbow is not a cloud; no color is a sound; the rocks are not trees. Sec. 

CHAPTER XIV. 

COMMENSURAL PROPOSITIONS. 

Having treated of the first four classes of propositions, we come now 
to commensural propositions. It must be evident to any one that if we take 
two simple existences which are inter se differentia, white and green for in- 
stance, we can not truthfully say that they are in any respect related to each 
other, except as colors; indirectly, as colors, they are similia, but directly, 
they are inter se differentia. Between two such existences, therefore, no com- 
parison can be made b} r which a result other than an heterical or differential 
one can be attained. They are not similia and therefore we can not by their 
comparison obtain a similical result; nor from their comparison can we ob- 
tain homon. After having obtained therefore, the results, homon, hetera, 
similia and differentia, in order to obtain, propositions, which will render 
results different from those just mentioned, we must measure inter se results 
already obtained. But homon can not be measured, for it is an identical 
thing, and a thing to be measured must be measured by some other thing. 
But hetera, as hetera, can not be measured, for in measurement there must be 
some coincidence and not mere separation, and differentia, as differentia, can 
not be measured, for they can have nothing in common which is measurable. 

Similia, therefore, are the only results, which admit of comparative 
measurement. We can say that this red is as red as that red, i. e., this red 
and that red are commensural, and if we compare one stick with another we 
can say that this stick i? as long as that one i. e., the lengths of the two sticks 
are commensural, and thus we can compare many of the similia of nature 
and obtain commensural results. We do not deem it necessary to enlarge 
upon the subject of commensural propositions, as we concluded that they 
will be easily understood, and they will also be illustrated along with the 
others hereafter. We must here observe, how 7 ver, that homon is at the bot- 
tom cf them. When we say, this red is as red as that red, the as red and 
that red are homon, and by stating two homonical propositions with the 
word as between them, we will readily see, how two homonical propositions 
merge into one commensural one: Thus, this red is red, as, that red is red. 
In the first proposition, the subject and predicate are objectionaly homon, 
and so also with the second proposition, and the word as shows that the two 
are commensural. We will subjoin a few examples for practice: The day 
was as dark as ni^ht; this candle shines as bright as that one; she looks as 
fresh as the rose; it is just as sweet as honey. x-f-N^-z. 



0" 
CHAPTER XV. 

INCOMMESSLRAL PROPOSITIONS. 

We come now to the consideration of incommensurable propositions, 
the last class of logical propositions. And in incommensural propositions, 
the existences compared are similia in kind, but the}' differ in degree or 
quantify. When we say that this candle shines brighter than that one, we 
mean that there is an excess of brightness in the one compared with the 
other. The t?ro are not differentials white and black are, but there is a 
difference, an excess, in the one over and above the brightness which exists 
in the other. The difference in the specific gravity of bodies is expressed in 
incommensural propositions, as sjold is heavier than iron, i. e., the specific 
gravity of gold and that of iron are incommensural. This excess in one of 
the existences compared is some times shown by the use of an adjective name 
in the comparative degree. There are, however, three ways of expressing the 
excess in words, viz., A is larger than B, B is lesa than A, ai.d B is not so 
large, or not as large as A. 

Now when we say that snow is white i. e., one of the facial gregaria of 
snow and white are nomon, we locale the gregarium, white among the other 
gregaria, which make up snow, so when we say that ice is colder than water, 
we locate the existence, which would be named by the adjective name in the 
positive degree in the subject ice, and by adding Kit or moke to this adjective 
name, and thus marking an excess, we locate also the excess in the subject. 
Take first the case of the comparison of simple existences, this red is reder 
than that red. Now leaving ER off of the adjective name and we will have 
before them, this red is red, an homonical proposition. And in the propo- 
sition this led is reder than that red, we retain the homonical red— the predi- 
cate of the homonical proposition, and add, KH to its name to snow an excess 
above the red which follows after than, and which is ihe predicate of the in- 
commensural proposition. But as the predicate of the homonical proposition, 
was located objectively in the subject of the proposition, i.e., it and trie subject 
were found to be homon,so the excess added to it in the incommensural pro - 

position must be located with it in the subject of the incommensural propo- 
sition. 

In the incommensural proposition, this red is less red than that red, 

however, the decrement is located in the subject and consequently the excess 

is in the predicate. And in the proposition, this red is not so red as that red, 

the so Kin and thal red are henmn, i. e., the degrees of red subjectively 

commensural are objectively homon in the predicate of the incommeusural 

proposition, and the particle not shows that the degrees in the subject and 

those in the homonical predicate are incommensural. In the commensural 

proposition, this red is as red as that red, the last two reds, which are homon 



es 

in the predicate, and the subject are commensural, but if we insert not we 
will have; this red is not as red as that red, in which the last/two reds are 
homon, and their degrees and those of the subject are incommensural, the 
difference or excess being in the predicate. 

Now when the subject is an aggregate existence and it is compared 
apparently with an aggregate existence in the predicate, in commensural and 
incommensural propositions, it is always one of the gregaria of each that is 
compared, and these gregaria compared are always similia in kind, but commen- 
sural or incommensural in decree. In the proposition snow is whiter than chalk 
tiie facial gregarium, white exists in each of the aggregate existences, but the 
degrees of white in the one and in the other are compared and found to be in- 
oommensura. And when we say all snow is whiter than chalk, it is one of the 
gregaria sine qua non of snow that enters into the incommensural proposition. 
And if we could say in truth that all snow is whiter than all or any chalk, 
the degrees ne plus ultra of chalk would be compared. 

Before passing on to the next chapter, we must examine such proposi- 
tions as; John is the strongest man in the house. This proposition at first, 
sight would appear to belong to a sevenih class of propositions, but on exami- 
nation, it will be found to be merely an homonical proposition collected into 
a conclusion from several incommensural ones, and it may be thus stated, the 
strongest man among the men in the house and John are homon. And so 
also, Sampson was the strongest man of whom we have read, is an homonical 
proposition. Hercules was stronger man Sampson, is an incommensural pro- 
position. And all propositions, in which there are superlative names, are 
homonical. We aj-ve the following examples for practice: Winter is colder 
than summer; the elephant is more intelligent than the ass ; dogs arc more 
faithful than cats; cows arc more useful than rabbits; the bite of a rattle- 
snake is mote dangerous to man than the sting of the wasp; Honey is sweeter 
than sugar; the note of the nightengale is more pleasaot than that of the 
crow : x-f-Y^ x. 

CHAPTER XVI. 

propositions piiOMiscrorsrv. 

Having gone through with the six classes of propositions, we should 
next in order consider their subdivisions into categorical and hypothetical; 
we do not deem it necessary, however, to do more than mention these subdivi- 
sions. Every one will see for himself that any propositioc of either of the 
foregoing elasses may be slated eategoricalh% i.e., the result be affirmed as 
actually existing, or a result may be supposed to ex'st for the sake of argu- 
ment. We will therefore, now give some further attention to the terms and 
copula of propositions of all the foregoing classes. 

And looking back to the nominal truths grounded in the non-cs:o, of 



69 
which we spoke at the beginning of our investigations, and supposing that 
all objects had had the same color, coald we have called this nominal 
truth a (one) color? We have already shown that the unit is a numerical re- 
lation and that our knowledge ot it is envoi ved from duality or plurality. 
And in the five nominal truths mentioned, we have hetera, from which the 
knowledge of first, second, third &c, might have been evolved. But 
we have also shown that when numbers, the names of the individuals of 
hetera, or of commensural colligations of hetera, are applied to existences, 
and the name to distinguish individuals otherwise than heterically, is spoken 
or written after them, the name so spoken or written must be the name of 
similia, a common name. We may h«ve a horse and a dog and the two are 
existences. But existence is not a name given to distinguish existences 
inter se, and should we write any name, which does distinguish existences 
inter se after the word two, we will rind that two will not apply unless tire 
existences be inter S3 similia. Horse and dog are differentia, and their 
names distinguish them ; neither of these names, therefore, tan be written 
after two so as to express to us the numerical sum of a horse and a dog; as 
hetera existences, two may be applied to them, but not as differentia. 

And respecting the nominal truths, as the are iuter se differentia, two 
could not be joined with any name, which distinguishes them as nominal 
(ruths. But if one be the name of a numerical relation, as we have shown 
when it is applied to a differential name, there must be more than one thing 
distinguished in like manner by the same name; there must be similia; 
otherwise the thing distinguished by such name could have no numerical re- 
lations to other things, except as hetera, which in language do not receive differ- 
ential names, which afterwards become the common names of similia. And 
therefore, when we say, Ax existence, by this expression we show that we 
have in our mind one of several or many existences, i. e., one of hetera, and 
'when we say a clog, the expression shows that we mention one of similia. 

Looking then at the nominal truth, color, could we say that, this is A 
(one) color? We think not. We could say this is color, or this is an exis- 
tence, and that is sound; but a color, as a name, not only distinguishes color 
from sound, taste, &c, but it also points out some one of similia, as colors. 
And hence a or an before a name, in homonical propositions, makes them 
quasi similical ; as this town is a Philadelphia, i. e., this town and one of the 
Philadelphia^ are homon, and in effect, this town and Philadelphia are simi- 
lia. The proposition This town is Philadelphia; is an homonical proposition 
but the placing of a before the predicate makes the proposition tnough ho- 
monical still, quasi similicai, there being but one Philadelphia in our mind, 
and this town not being that one. 

And all names excepting proper names, used as terms of propositions 
point out among other things a numerical relation inter similia. In the 



70 V 

homonical proposition, John is Job;.; neither of the terms point out a nu- 
merical relation; but in the homonical proposition J dm is a man; i. e., John 
and a (one) man are homon, the predicate term joints out a numerical rela- 
tion, and as it stands tor the same object as John, when John is brought 
among the similia of which it is one, among these objects, John has a 
numerical relation, he is a man, one of the similia named man. 

Now bringing before us again the name color, if there existed a red 
and A green, we would then have two colors and we r.ould say that red is a 
color and also that green is a color; but upon the. principle just exhibited 
above were there but one red object and one green object in existence, red 
and green would be proper names and we coi.ld not say, this is a red, or that 
is a green, though we could say this is a red color and that is a green color. 
J>ut in the homonical proposition Red is a color; red is brought from pri- 
mary propositional truths into nominal truths, and among nominal truths, it 
is one of the similia, a color, i. e., red and a (oae) color are homon. But if 
red be a color, how can we fully distinguish m every respect this existence 
from others by words, when *e have it in our minds, otherwise than by cal- 
ling it a red color V And hence we see that every term of a proposition, 
which is made up of more than one name of simple existences, points out 
the results of several relations, and the numerical relation among similia 
pointed out by the term, is called the extension of the term. 

Passing on now to Hie consideration of terms, which are the names of 
aggregate existences, take the proposition, Snow is white; i. e., a gregarium 
of snow and a white color are homon, and we see that white is brought 
into and fasciculated among other gregaria in snow by an homonical pro- 
position. Again, Snow i^ cold, Snow will nidi, &c., are all homonical pro- 
positions, and the predicates of all these j roposiiions are located, fasciculated 
in snow. We may say White is in snow; i. e., the where of a white and that 
of snow are homon, Cold is in snow, The capacial gregarium of melting is in 
snow; all those gregaria co-exist in snow, i. e., a fasciculus of certain grega- 
ria and snow are homon. And if by homonical propositions we fasciculate 
simple existences in an aggregate one, can we not in like manner bring 
together aggiegate existences? When we say, The audience was intelligent, 
we have done so. John is intelligent, VXilliam is intelligent, Mary is intelli- 
gent, &cv; but John was one of the audience, William was one, cv:c. 

And when a name, as the term of a proposition, stands for an aggregate 
existance, the gregaria taken together in tasciculo constitute what is called 
the comprehension of the term. And in the differential proposition, Stone 
is not iron, the comprehensions of the terms, stone and iron, i. e , the 
gregaria of the one and those of the other, are compared in fascicnlo. Some 
of the gregaria of the one and some of the other may be similia; but if the 
one comprehend certain gregaria and the other certain gregaria, which 



71 
are inter se differentia, or if the one contain gregaria over ami above the 
sum o( the gregaria contained in the other, the two fasciculi are inter se 
differentia, and they are differentia throughout the whole extent of the> 
similia of the one and of the other. Stone is not iron is equivalent to, Ail 
stone is not iron ; better, No stone is iron ; and this proposition is equiv.Lmt to 
Xo iron is stone. And hence when fasciculi of gregaria comprehended by 
the subject and predicate terms, are compared, the proposition may always 
be converted, i. e., the subject be made the predicate and the predicate the 
subject. This is also the case when simple existences are compared. Red is 
roc]^ homonical ; This is not that, That is not this, helerical ; Red is not green, 
Green is not red, differential ; This is like that, That is like this, similical ; This 
red is as red as that, Thai red is as red as this, commensural ; and This red is 
not so red as that, That red is reder than this, incommensural. But when 
one term is the name of an aggregate existence and the other the name of a 
simple existance, it is always one of the gregaria of the aggregation that is 
compared with the simple existence pointed out by the Other term, as we 
have already seen: Snow is white, means that the color of snow is white 
which may also be converted into \Vhfte is the color of snow. John is a 
man, may be converted into One man is John. And hence in order to ascer- 
tain the existences, which are really compared in any proposition, construct 
one of the terms, if necessary, so that the terms may then be transposed and 
give the same result as before. This may be none in all propositions. 

Now prepositions as we have heretofore said, are names of relations 
in. space among existences: thus when we say Snow is white, we mean that 
the color of snow is white, and snow being the name of a faciculus gregaria, 
of shows that COLOR is located as one among the gregaria in fasceculo dis- 
tinguished try the word snow: it, that is the preposition of, is the name given 
to the relation of color among the oilier gregaria in space. And hence there 
is no difference of affirmation between Snow is white, and The snow upon 
I lie mountain is white; the affirmations are similia. But in the latter pro- 
position One ot the gregaria. of snow upon the mountain is white; in the 
subject we have a numerical relation (one) existing among simple existence* 
(gregaria) located in an homonical where (in snow) and named snow, which 
where is objectively homonical with another where indicated by Upon the 
mountain. But a (one) is not the existence compared with wdiite; the name 
white is differentia; one distinguishes hetera and points out the relation 
among similia, while the proposition is homonical; neither is any where 
compared with white, for where and white are differentia, while the 
proposition is homonical; snow is not compared with white, but the color of 
snow ; nor is the mountain compared with white; there is nothing, therefore, 
in either of the foregoing propositions compared with white besides a color. 
All the words, therefore One of the gregaria of the snow upon the mountain; 



taken together, constitute but one name to distinguish one simple existence 
in every respect from others, and which simple existence we compare with 
white and pronounce them to be objectively homon. 

If a, b, c, d and e be th^ simple existences, the gregaria of an aggre- 
gate existence, and A be the name of the fasciculated gregaria, we may then 
say according to the custom of language that A is a, A is b, etc. And if we 
wish to locate A in a some where, which shall be distinguished from other 
wiieues by words we may say; A upon the table is a. And if the where is 
not yet sufficiently distinguished, and we may say, A tpon the table in the 
house; and still further, A upon the table in the house of John Stiles on 
front street between Walnut and Chestnut streets in the city of Philadelphia 
is a. But again, take the proposition, John's book is on the table; and we 
see that the subject of this proposition is a faseiculalion of the subject and 
predicate of the proposition, This book is the property of John. We do not 
consider it necessary to explain the terms of propositions further: but the 
copula is yet to be examined. 

Now in the propositions, I am; 1 exist, or I am an existence; we must 
see that the affirmation is made in the present tense, grammatically. And 
in the proposition, I was, Did exist, or Was an existence; the affirmation is 
also made at the present time, but the time of existence spoken of, is the 
past. I was an existence; may be rendered, The time of my existence of 
which I speak, and past time are homon. Columb is discovered America, A 
J). 1492; may be rendered The time of the discovery of America by Colum- 
bus and A. D 1402 are homon, etc. And whatever may be the tense of the 
verb, the existences are always compared and the affirmation made at the 
present time. But respecting what is called the potential mode by gram- 
marians, as John may be a scholar; the vert) itself implies 3apac4al gregaria; 
Ihecapacial gregaria of John and those of a scholar aresimiiia; and in the 
proposition, John might have been a scholar; the capacial gregaria are re- 
fered to as having existed in past time. 

Now in all propositions, we say that the copula ts, means exists But 
take the proposition, Nothing is nothing; and if is means exists, what is it 
that does exist, for nothing can not be an existence? But we say ihat it is 
the relation between the subject and predicate that exists. But still it will be 
asked the relation of what, when we say Nothing is nothing? And in order 
to understand this, it is necessary to consider how we came by the name no- 
thing. Take the proposition This is nothing, i. e., This thing and no-thing 
are homon. Now if the subject this thing, means some thing and the 
predicate nothing, means no-thing, how can the two be homon ? It' we con- 
ceive of a witch, an old hag of a" woman, with a beard, riding a broomstick, 
subjectively this is some thing, but objectively it is nothing, and therefore, 



=" 



we can say with truth that this some thing grounded in the ego, is upon the 
ground of the non-ego nothing; this is nothing. 

"Rom. — "Peace, peace, Mercutio, peace; Thou talketh of nothing." 

"Marc. — True, I talk of dreams, which are the children of an idla 
brain, begot of nothing but rain fantasy.^ 

4 Now had man gained the knowledge of only two objective existences 
and had he called the one a, not a would have been a name sufficient to dis- 
tinguish the other, and he then could hare said pointing to a, This is a, and 
pointing to the other, This is not a; for if it be not a, it must be the other ex- 
istence. Both these propositions then would be homonical viz: This is a, 
this aud a are homon ; This is not a, this and not a are homon. But if he 
wished to show a, and not a to be differentia, or to affirm hetera in a proposi- 
tion, he weuld have to say, a is not not a, i. e., a and not a are hetera, or a and 
not a are differentia. But if there were four or five existences known to man 
and he should distinguish one of them by the name a, and then pointing to 
another he should say, this is not a; not a, would not distinguish any one of 
the remaining four from the others, and consequently not a would be indefi- 
nite. And hence wheo there are two existences or but two modes of «xis- 
tence, and the one is named a. for instance, not a may be used as a definite 
name for the other, as truth, not truth—error; faculty of vision, not faculty 
of vision — blind; hearing, not hearing — leaf, &c. Bat when there are more 
than two existences or modes of ex i stance, not, ux, in dis, &c, joined to 
names makes an indefinite uanve. •'• ' ••• 

Bu^suppose that we had the knowledge of but two existance*, which 
were inter se differentia, aud we should give to each of them a separate name, 
as red and green for instance, we would then say red is not green. But not 
green, if it be any thing, must under the supposition, be red, and we could 
say, not green is red, i. e., not green and reef are homon. But if we had a 
knowledge of three differentia, red, white and green, for instance, and we 
should say that red is not green, not green would stand for either red or 
white, and would b« indefinite. But what definite existence is meant in the 
ease, by not green, would be indicated by the subject of the proposition, 
red, and hence red and the not green are homon. Ana if not green and 
red be homon in the proposition, red is not green, red and green must be 
differentia: for in this proposition, red and not green are homon, and in the 
proposition, green and not red aie homon, .green is, and red is; the homoni- 
cal proposition, red is green, however, is not true, and the similical proposi- 
tion, red is like green is also untrue, and hence we see how homon lies at 
the foundation of all propositions; and we see also that the pai tides not and 
no, belong always to the subject or predicate and never to the copula. 

We have now gone far enough, perhaps to make our news of proposi- 
tions be understood; yet it may be said that when we say snow is white and 



74 
we change the wording of this proposition into One of the gregaria of sno »v 
and white are homon, we have hut changed a simple proposition into a 
complex one ; such however is not the case. When we say Edward and 
John are good, we can fully express in two proposition the meaning of the 
above phraseology, as Edward is good and John is good. But when we say 
One of the gregaria of snow and white are homon, we can not resolve this 
into two propositions and say One of the gregaria of snow is the same thing 
and white is the same.thing, with any sense; neither can we resolve This grain 
of wheat and that grain of wheat are similia, into This grain of wheat is 
similia and that grain of wheat is similia. And if we are right and we are 
understood in our views of propositions, we think it will not be difficult to 
explain hereafter the syllogism in all its modifications and functions. 

CHAPTER XVII. 

THE SINGULAR SYLLOGISM. 

In every legitimate syllogism, there must be two and only two propo- 
sitions, which are called the premises, and a conclusion drawn from these 
premises. It is also necessary that there be four subjectively heterical exis- 
tences, two of which, one in each premise, must be objectively hetera, and 
two of which must be objectively homtn, or similia or commensura inter se, 
and that the other two apear in the conclusion. The name of the homon i- 
cal existence, or of the similical or commensural existences, which are in the 
premises, but not in the conclusion, is called the middle term, because it 
designates or distinguishes the homonical existence or the similia, or com- 
mensura, with which, each of the existences, which appear in the conclu- 
sion has been compared, and it is by means of thi? homonical existence or 
similia or commensura designated by this that middle term, the comparison, 
between tha other two existences is effected and the result set down in the 
conclusion. Now it must appear upon the principle of pormutation that, if 
a, b and c be the terms of the premises, and we arrange a and b together and 

a and c together, we can have four and only four different arrangements in 
the premises; thus, a b, b a and a c, c a. And hence logicians have divided 
syllogisms into four figures, as they are called, according to the positions 
occupied by the middle term in the premises. This middle term may denote 
the subjects of both propositions, or premises, the predicates of both, or the 
subject of the first and the predicate of the second, or the predicate of the 
first and the subject of the second. And hence let a, or a and a when similia 
or commensura are used be the middle term, and the following paradigm will 
show the figures : 






1st figure. 


2d figure. 


3d figure. 


4th figure. 


A isB 


Bis A 


AisB 


B is A 


Cis A 


Cis A 


A is C 


AisC 


.\C is B 


.\C is B 


.\C is B 


.\C is B 



75 
Now if we take the first four classes of propositions these may be 

combined two and two as premises, and hence the first figure will give six- 
teen modes of syllogising according to the different manner in which we 

combine these four classes of propositions and so with the other figures. 
The following paradigms will show the maimer of combining the first four 
classes of propositions in all the figures: 

FIRST FIGURE. 



First mode. 

A & B are homon, 
O&A 4 " homon. 
.-.CAB u similia. 



Second mode. 
A & B are hetera, 
C & A are hetera, 
•% C & B are hetera 



Third mode, 

A & B are similia 
C & A are si nilia, 
.*. C & B are similia. 



Fourth Mode. 

A & B are differentia, 
C & A arc differentia, 
.•. C&B " differentia, 
or similia. 



5th. 
A & B are homon, 
C & A are hetera, 
.*. C & B are hetera. 



8th. 

A & B are hetera, 
C & A are homon, 
.*. C & B are hetera. 



6th. 

A & B are homon, 
C & A are similia, 
.*. C & B are similia. 



9th. 
A & B are hetera, 
C & A are similia, 
.-. C & B are similia or 
differentia. 



7th. 

A & B are h»men, 
C & A are differentia, 
.*. C & B are differentia. 



10th. 

A & B are hetera, 
C & A are differentia, 
.*. C & B are differentia 
or similia. 



11th. 

A & B are similia. 
C & A are homon, 
:. C & B are similia. 



12th. 

A & A are similia, 
C & A are hetera, 
.*. C & B are similia 
differentia. 



or 



13th. 

A & B are similia, 
C & A are differentia, 
.-. C & B are differentia. 



14th. 

A & B are differentia. 

C & A are homon, 

;. C & B are differentia. 



loth. 
A & B are differentia, 
C & A are hetera, 
/. C & B are differentia 
or similia. 



16tlf. 

A & B are differentia, 

C & A are similia, 

.*. C & A are differentia. 



MODES OF FIGURE SECOND. 



1st. 



2nd. 



B & A are homon, ; B & A are hetera, 
C ifc A* u similia, J C <fc A are hetera, 
.-. C & B - 4 similia. .'. C & B are hetera. 



3rd. 

B & A Are similia, 
O&A are similia, 
.*. C & B are similia. 



4th. 

B & A are differentia. 
C & A are differentia, 
.*. C & B are diff. or sim 



76 



5th. 

B & A are homon, 
C & A are hetera, 
.-. C & B are hetera. 


6th. 
B & A are homon, 
C & A are siniilia, 
.-. C & B are similia. 


7lh. 

B & A are homon, 
C & A are differentia, 
.*. C & B are differentia. 


8th. 
B & A are hetera, 
V & A are homon, 
A C & B are hetera. 


9th. 

B & A are hetera, 
C & A are similia, 
.-. (J & B are sim. or diff. 


10th. 
B & A are hetera, 
(J & A are differentia, 
.-. C & B are diff. or sim. 


11th. 
B & A are similia, 

.*. C & B are similia. 


12th. 
B & A are similia, 

.*. C «fc B are sim. or diff. 


13th. 
B & A are similia, 

.*. C & A are differentia. 


14th. 

B <fe A are differentia, 
V & A are-lioraon, 
■/. C*fc Bare differentia. 


15th. 

B & A are differentia, 

C & A are hetera. 

.'. C <fc B are diff. or sim. 


16th. 

B & A are differentia, 

C & A are similia, 

.-. C & B are differentia. 



MODES OF FIOUKE THIRD. 



1st. 



2nd. 



A & B arc homon, i A & B are hetera, 
A* & C are homon, A & C a e hetera, 
.*. C «fc BaresimiJia .*. O & B are hetera. 



3rd. 

A & B are similia, 
A & C a iv i-imilia, 
.*. C & B are similia. 



4th. 

A & B are differentia, 
A «fe C are differentia, 
.*. C &-B are diff. or pirn. 



5th. 



A & B are homon, 
A & C are hetera, 
.-. A & B are hetera. 



6th. 

! A&B are homon, 
! A & C are similin, 
! .*] C & B are similia. 



'Hi. 



i A & B are homon, 
[ A & C are differentia, 
i .* C & B are differentia 



8th. 

A & B are hetera, 
A & V are homon, 
.*. C & B ape hetera. 



9th. 

A & B are hetera, 

A & C are similia, 

. . & B are sim. or diff 



10th. 

A & B are hetera, 
A tV C are dinerentia, 
.-. C & B are diff. or sim. 



lllh. 

A & B are similia, 
A & are homon, 
.-. C & B are similia. 



12th. 

i A & B'are similia, 

j A *fc are hetera, 

! .*. C & B are sim. or diff 



13th. 

A & B are similia, 
A & are differentia, 
. . C & B are differentia. 



14th. 

A & B are differentia, 
A & C are homon, 
.-. V ■& B are differentia 



15ih. 

A & B are differentia, 

A & are hetera, 

.-. & B are diff. or sim. 



6ih. 

A & B are differentia, 

A & C are similia, 

.*. & B are differentia. 



77 



MODES OF FIGURE FOURTH. 



1st. 

B and A are hornon, 
A 1 and C are homon, 
.'. C and B are siniilia. 



2d. 

B and A are hetera, 
A and C are hetera. 
.-.C&B are hetera. 



3d 

A andB are similia, 
A and C are similia. 
.*. C&B are similia. 



4th. 

B & A are differentia, 
A & C are differentia, 
.-.C&B arediff. orsim. 



5th. 

B and A are hornon, 
A and C are hetera, 
.-. C and B are heten 



6th. 

B and A are homon, 
A and C are similia, 
.-. C and B are similia. 



7th. 



B and A are homon, 
A aud C are differentia, 
.*. C and B are differentia. 



8th. 

B and A are hetera, 
A and C are homon, 
.*. C and B are hetera. 



9th. 

B and A are hetera, 
A and C are similia, 
.-.C&B are sim. or diff. 



10th. 

B and A are hetera, 
A and are differentia. 
.-.C&B are diff. or sim. 



11th. 

B and A are similia, 
A and C are homon, 
.-. C and B are similia. 



12th. 

B and A are similia, 
A and C are hetera, 
.-. C&B are sim. or 



diff. 



13th. 

B and A are similia, 
A and C are differentia. 
.*. C and B are differentia. 



14th. 

B and A are differentia, 
A and C are homon, 
.-.C&B are differentia. 



loth. 

B and A are differentia, 
A and C are hetera, 
.-.C&B are diff. or sim, 



16th. 

B and A are differentia, 
A and are similia, 
.-.C&B are differentia. 



To the foregoing paradigms, we will add another in which the existen- 
ces are distinguished by their names, but without regard to figure. 



1st. 
Snow is white — homon, 
The foam of the seas is white — homon, 
Therefore, the colors of snow and of 
the foam of the sea are similia. 



2d. 
This marble is not that one — hetera, 
The other is not this one — hetera, 
Therefore, the other one and that 
one are hetera. 



3d. 
The color ot John's hair is like Ma- 
ry's — similia, 
Mary's is like James' — similia, 
Therefore the colors of John's and 
Jamas' hair are similia. 



4th. 
An apple is not a peach— differentia. 
A pear is not an apple — differentia, 
Therefore a pear and a peach are dif- 
ferentia or similia. 



5th. 
Loaf sugar is sweet — homon, 
This loaf is not that apple— hetera, 
Therefore, the taste of sweet in this 

sugar,.and the taste of that apple are 

hetera. 



6th. 

Sugar is sweet— homon, 
This bread tastes like sugar — similia, 
Therefore the taste of this bread and 
sweet are similia. 



78 



7th. 
Sugar is sweet— honaon, 
Vinegar is not sweet — differentia, 
Therefore the tastes of sugar and of 
vinegar are differentia. 



8th. 
This biscuit is not that one— hetera, 
This biscuit is sweet — homon, 
Therefore the sweet of this biscuit 
and the taste of that one are hetera. 



9th. 
This apple is not that one— hetera, 
This pear tastes like that apple— sim. 
Therefore the tastes of this apple and 
this pear are similia, or differentia. 



10th. 
This apple is not that one— hetera, 
This pear does not taste like that apple 

— differentia, 
Therefore the tastes of this apple and 
of this pear are differentia or similia. 



11th. 

This cake tastes like sugar— similia, 
Sugar is sweet — homon, 
Therefore the sweet in sugar and the 
taste of this cake are similia. 



12th. 
The color of the barn is like that of 

the house— similia, 
John's barn is not the barn spoken of 

— hetera, 
Therefore the colors of John's barn 
and of the house are similia or diff. 



13th. 
The color of the barn is like that of 

the house — similia, 
The color of the stable is not like that 

of the house — differentia, 
Therefore the colors of the barn and 

stable are differentia. 



14th. 
Sweet is not sour — differentia, 
Sugar is sweet— homon, 
Therefore the taste of sugar and sour 
are differentia. 



15th. 
This cake is not sweet- 



■differentia, 



This bread is not the cake — hetera, 
Therefore, the taste of this bread and 
sweet are differentia of similia. 



16th. 
This cake is not sweet— differentia, 
This bread tasies like the cake — sim. 
Therefore the taste of this bread and 
sweet are differentia. 



Now from the foregoing paradigms, we see that like numbered modes 
in each figure give like results in the conclusion and that in each figure we 
obtain eleven categorical and five disjunctive conclusions. From homoni- 
cal premises (1) we obtain similia in the conclusion; from heterical premises 
(2) hetera; from similical premises (3) similia; from differentia premises (4) 
differentia or similia; from homo-heterical premises (15 and 8) hetera; from 
homo-similical premises (16 and 11) similia; from homo-differentia premi- 
ses (7 and 14) differentia; from similo-heterical premises (9 and 12) simi- 
lia or differentia; from similo differential premises (13 and 16) differentia; 
and from heterico differential premises (10 and 15) differentia or similia; in 
all clearer categorical and fine disjunctive conclusions. And of the catego- 
rical conclusions, four are similia, three are hetera and four are differentia. 
Now the foregoing figures with their modes exhaust the power of syllogising 
with the first four kinds of propositions, in the singular syllogism. 



79 



But the fifth and sixth classes of propositions may be combined with 
homonical and heterical propositions, in figures and modes similar to those 
already exhibited. And letting A stand for the middle term, as before, the 
following paradigm will show the combinations in the first figure. And 
with the fifth and sixth classes of propositions we may use the sign = equal 
to, between commensura, and > or < the sign in commensura, just as in 
mathematics. 



1st. i 

A& B are hotnon, 

C &> A' are homon, j 

.-. C=B. ! 


2d. 

A & B are hetera, 
C & A are hetera, 
.-. C & B are hetera. 


3d. 

A=B, 
C=A, 
.-. 0=B. 


4th. 
A>B j A<B i A<BorA>B 
OA C<A OAorC<A 
.\OB j.\C<B | .\C=Bor C<Bor OB 


5th. 
A and B are homon, 
C and A are hetera 
,\C and B are hetera. 


6th. 
A and B are homon 
C=A 


7th 
A and B, are homon, 
C<A, lor OA 
.-.C<B ;.\OB. 


8th. 
A and B are hetera, 
C and A are homon, 
.-.C and B are hetera, 


9th. 
A and B are hetera, 
C=A 
.-.C=Bor C<Bor C>B. 


10th. 
A and B are hetera, 
OA | or C<A, 
.-.C=B, or C>B, or C<B, 


11th. 
A=B, 

C and A are homon, 
.\OB. 


12th. 
A=B, 

C and A are hetera, 
.\C=B, or C<B, or OB. 


13th. 
A=B, 

C<A, : or OA, 
.\C<B, ;/.OB. 


14th. 

A>B, or A<B, 
C and A are homon, 
.\OB ! .\C<B, 


15th. 

A>B j or A<B, 
C and A are hetera, 
.•.C=B, orC<B, or OB. 


16th. 

A>B orA<B, 

c=a ; C=A, 

.\U>B ' C<^B. 



We do not deem it necessary to give paradigms of the modes of the 
remaining three figures in which homonical, heterical, commensural and in- 



80 
cominensural propositions are combined. Now the four figures with their 
modes, in which the first four classes of propositions are combined and the 
four figures with their modes, in which homonical heterical, cominensural 
and incommensural propositions are combined, exhaust the whole power of 
syllogising in singular syllogisms, i. e., in comparing two existences by the 
means of an homanical existence or of two similical or commensural exis- 
tences. We hove not put the words — all, every, no &c, before any of the 
terms, because these words, as we have heretofore shown, do not change the 
character of the affirmation, but belonging to the terms they are used to dis- 
tinguish and characterise the existence, which we are comparing, and they 
may be thrown out of every proposition, in which they occur, excepting 
numerically complex propositions, by changing the wording of the proposi- 
tion and without affecting the result; as all men are mortal, is equivalent to 
man is mortal, i. e., one of the gregaria sine qua non of man and mortality 
are homon. The propositions, All the Apostles were Jews; All the boys in 
the room are barefooted, &c, are numerically complex propositions, and they 
are not used in the singular syllogism The words— some, most, a few, &c, 
also distinguish merely the numerical relations inter similia upon a certain 
generalization. And by the custom of our language, every proposition, in 
which they occur, may be stated in other words, which shall not express, but 
imply their substance ; as some apples are sour, into all apples are not sweet; 
i. e., sw 7 eet and sour are not gregaria sine qua non of apples. And hence,. 
some, most, a few, &c, show, in propositions, an indefinite numerical rela- 
tion among apples, for instance, which as apples are similia, but which, 
outside and over and above the gregaria, sine quibus non, possess other gre- 
garia, which, when considered, enables us to distinguish and further 
differentiate. 

CHAPTER XVIII. 

EXPLANATION OF THE SYLLOGISM. 

If a man were in a wood among fallen timber and found two logs, 
which he was unable to lift, and whose comparative lengths he desired to 
know, without the use of the- syllogistic process he would not be able to ac- 
complish his object. If however, he should cut a rod, which we will call A, 
he could go with it to the first log, which we will mark 1st, and find that 1st 
and A are commensura, and then with his rod he could go to the second log, 
which we will mark 2d,. and find that 2d and A are commensura and then he 
would have the premises of a syllogism: 1st and A are commensura, 2nd 
and A are commensura, therefore 1st and 2d are commensura; or lst=A, 2j> A, 
if it be so and therefore 2d>> 1st. And without the power to syllogise the car- 
penter could make no use of his foot-rule, the shoemaker no use of his last, the 



81 

farmer no use of his lialf-bushel ; no one could put into a pile one cord of wood ; 
and no one could tell without first having knocked his hat off,whether the door 
in his house was high enough to let him enter without bending his body. The 
process of syllogising is used by every person in the daily vocationg of life,, 
and it always has been so used from the creation of man. 

But notwithstanding the almost constant use of the syllogism by all 
men, the process'itself has been misunderstood both by the friends and the 
enemies of logic. The opposers of logic have represented that if the syllo- 
gism be a true process of reasoning used by us in matters about which we 
reason, men could not have reasoned at all before the time of Aristotle, who 
is regarded as the true expounder of logic; which is argument is analogous 
to the following; If the wiieels of a wagon tarn upon the principles of the 
lever before these principles were understood men could not have driven 
wagons. The contempt, however, which the opposers have heaped upon 
logic, and of which its friends complain, is not owing to the want of a syllo- 
gistic process in the mind, but to the circumstance that the friends of logic 
have been neither able to explain this process, nor to refute the objections of 
its advisaries. 

For the explaination of the syllogism, most of the writers upon logic 
have relied upon the Aristotlean dictum de omne et nullo — what ever can be 
predicted of a class can be predicted of any individual of that class — and 
hence they say that the middle term must always be distributed in one of th« 
premises by being the subject of a universal affirmative or the predicate of a 
negative proprosition, which in our opinion amounts to nothing so far as the 
syllogistic process itself is concerned. For a class is nothing else than 
several individuals inter se similia, or but one individual differentiated from 
all other things; and hence the dictum asserts merely that whatever can be 
predicated of each one of similia can be predicated of any one of similia; 
and although this is true, it is but a part of the whole truth. If we have be- 
fore us several marbles, the colors of which are inter se similia, we may with 
equal truth, turn the dictain the other way, and say that whatever can be 
predicated of the color ot any one of the class, can be predicated of the 
color of each one of the class, for. the reason that the colors are inter se 
similia. And for the same reason and for none other, to-wit, that the indi- 
viduals are similia in the respect in which every one or any one is spoken 
of, or joined with a certain predicate in a proposition, does the dictum mean 
anything: that there actually are in nature similia, differentia, commensura 
and incommensura, is the foundation of the dictum, and yet a syllogism may 
be coostructed of homonical or heterical premises. And from the notion 
that in every syllogism tha middle term must be be distributed in one of the 
premises, i. e., stand for a whole class of individuals eo nomine et innumero; 
while in truth it is never does so stand, but always represents an homonical 



individual, or an individual of simiiia, or of commensura, the friends of logic 
have been overpowered by their own logic. And hence the friends of logic 
have conceeded to its adversaries, that in every legitimate syllogism, the con- 
clusion contains nothing which is not emplyed and virtually asserted in the 
premises. For say they we reason from generals to particulars, and what is 
true in general is true in particular — dictum deomni et nullo. And although 
J. Stuart Mill was able to see that Aristotle's dictum was only adapted "to ex- 
plain in a circuitous and paraphrastic manner the meaning of the word 
class." Yet he too along with the rest was overpowered by the dictum. 
And hence he says "It must be granted that in every syllogism considered as 
an argument to prove the conclusion, there is a petitio principii. When we 
say all men are mortal, Socrates is a man, therefore Socrates is mortal, it is 
unanswerably urged by the adversaries of the syllogistic theory, that the 
proposition, Socrates is mortal, is presupposed in the more general assump- 
tion, all men are mortal ; that we could not be assured of the mortality of all 
men, unless we were previously certain of the mortality of every individual 
man; that if it be still doubtful whether Socratee, or any other individual 
you choose to name, be mortal or not, the same degree of uncertainty must 
hang over the assertion, xlll men are mortal; that the general principle, in- 
stead of being given as evidence ©f the particular case, can not itself be 
taken for true without exception, until every shadow of doubt which could 
affect any case comprised with it is dispelled by evidence aliunde and then 
what remains lor the syllogism to prove ? That in short, no reasoning from 
generals to particulars can, as such, prove any thing; since from a general 
principle you can not infer any particulars but those which the principle 
itself assumes as foreknown. This doctrine is irrefragable." 

Now this "irrefragable doctrine" is owing to a misconception of the 
nature of propositions and of their combinations in the syllogism. In the 
first place it is not true, although it has generally been conceeded to be so, 
that there is nothing contained in the conclusion, which is not implyed in 
the premises. In the syllogism, A and B are simiiia, C and B are simiiia, 
therefore C and A are simiiia, we have indeed the existences A and C in the 
premises, their relation, however, to each other, is neither expressed nor im- 
plyed in either of the premises, but it is evolved from the combination of 
the premises. And if it be meant that by the combination of the premises 
the conclusion is implicated, this indeed is true, but this certainly can not be 
urged as an objection, for it is of itself an approval of such combination for 
the purpose of gaining a result, which we can not obtain without such 
combination. In order to understand this matter clearly, it is necessary that 
we enter into an elaborate explanation of the syllogism. We have shown 
heretofore that when the existences really compared in any proposition are 
clearly set out by the wording of such proposition, the terms of the proposi- 



83 

tion may be transposed; as all men are mortal, i. e., one of. the gregaria sine 
qua non of man and mortality are homon, and by transposition, mortality 
and one of the gregaria sine qua non of man are homon. And hence when 
a proposition is so worded that the terms may be transposed (and every pro- 
position can and ought to be so worded when it is considered in a scientific 
view) it may be combined with another proposition worded in like manner, 
in any one of the four figures; and therefore, an explanation of the syllogism 
in any one of the sixteen modes of any figure, will be an explanation of the 
like numbered modes in all the figures. 

V\e will commence our examination, therefore, with mode 1st in the 
paradigms in which the first four kinds of propositions were used. Take the 
syllogism, All snow is white or snow is white, The foam of the sea is white, 
therefore the colors of snow and of the foam of the sea are similia, 
i. e., snow and the foam of the sea are similia in one facial gre- 
garium — color — which facial gregarium of snow and that of the foam 
of the sea, have each of them oeen differentiated from the other four 
nominal truths into color; but inter se they could not be differentiated, and 
therefore they are similia. But we have heretofore shown that netera li3 at 
the very foundation of our knowledge. Suppose then that we look at the 
color of paper, and without any reference to discrimination say— this is — 
and having turned our eyes away from it, look at the same paper again and 
say — this is; now is this the thing which, we have said, is, when considered 
as grounded in the ego, the same thing in both cases? certainly not; and why 
not? Simply for the reason that their times can be heterated, and the power 
of our minds to heterate, gives us the knowledge that then and now are 
hetera and that an existence grounded in the ego five minutes ago is not sub- 
jeclively the same existance grounded in the ego now. But if two existences 
can be heterated only, the two must be to us inter se similia; and therefore 
when we have said, this is, and that is, if we can discriminate no farther 
we must say, this and that are similia, and merge the two homonical propo- 
sitions into one similical proposition. Returning therefore to the premises, 
Snow is white, The foam of the sea is white, the heterical whites are similia 
we can discriminate them no farther than into hetera, and hence the conclu- 
sion must follow that the color of snow and that of the foam of the sea are 
similia. But when we say, Snow is white, The foam of the sea is white, 
therefore the colors of snow and of the foam of the sea are similia, we must 
recollect that the heterical whites, which are subjectively similia, have, 
each of them, an objective where, and therefore they are also objectively 
similia, while if we should project them into an homonical where, they 
would be objectively homon. The above premises, therefore, contain four 
subjective existences, two of which the heterated whites, are subjectively and 
objectively similia; objectively however, there are but two existences in the 



84 
premises to wit, the color of snow and the color of the foam of the sea; and 
objectively the syllogism in mode 1st, in the conclusion locates these objec- 
tive existences, as similia in their respective wheres. 

Mode 2d, if we consider the four hetereical existences of the premises 
merely subjectively, they would not bring us into a conclusion; but two of 
the subjective existances must be considered as occupying an homonical 
where in an homonical time; they must be objectively homon. When we 
say 1st and 2d are hetera, 3d and 2d are hetera, therefore 1st and 3d are hetera, 
the two subjective 2ds must be referred to an homonical where at an homoni- 
cal where at an homonical time; but 1st and 3d, cannot be homon for they 
are not compared with each other in either of the premises, but they are 
brought together by means of 2d, and if 2d and both 1st and 3d, be hetera, as 
stated in the premises, 1st and 3d must also be hetera. It may, however, be 
said that in this mode the conclusion does not follow from the combination 
of premises; tor, if we put before us three objective existences, marked 1st 
2d 3d, we can say first is not third, without comparing each of these with 
second. This is true; but it is the distinguishing terms, 1st and 3d, which 
enable us to jump the middle existence. Suppose we apply our nose to a 
rose and say This (1st) smell is not that scent, we then apply our nose again 
and say, This (2d) smell is not the 1st smell, therefore 2d smell and that scent 
are hetera. In this case the 1st smell, which is the middle existence appears 
twice subjectively, but we refer these two subjective existences to an homoni- 
cal where and time, and therefore they are homon, and without this middle 
existence we could not gain the conclusion, that second smell, and that 1st 
scent, the homonical scent mentioned in the first premise, are hetera. 

In mode 3d, each of the premises is a conclusion drawn from a former 
syllogism: as A is white, B is white, therefore the colors of A and B are 
similia, (mode 1st); A is white, C is white, therefore the colors of A and C 
are similia (mode 1st); and from these conclusions we form the premises, A 
and B are similia, and A are similia, and hence C and B are similia — con- 
clusion. Mode 3d needs no further explanation. 

Mode 4th is somewhat more difficult. When we say, sweet is not sour, 
bitter is not sweet, we are apt to look back at the words sour and bitter, and 
as these words distinguish differentia, we see from the terms that sour and 
bitter are differentia, and hence we are apt to infer merely differentia from 
the premises. When we say, A peach and a pear are differentia A potato and 
a pear are differentia, we will naturally say, A potato and a peach are differ- 
entia, which indeed is true, but it is not therefore true, it does not follow 
from the. premises. No categorical conclusion can he legitimately drawn 
from these premises, the conclusion which really does follow, is that a potato 
and a peach are either differentia or similia. This will easily be seen if we 
treat a peach and a potato merely as hetera and call the peach first, and the 



85 

potato second*: then dismissing from our mind those differential names, we 
say, 1st and a pear are differentia, 2d, and a pear are differentia, and as we do 
now see from the terms 1st and 2d whether they be differentia or not, the 
conclusion follow r s ligitimatelyin our minds from the premises, and we con- 
clude that 1st and 2d are differentia or similia. 

The fifth and eighth modes, which are in substance alike, are easy. 
The color of this marble is white, the color of this marble and the color of 
that one are hetera, therefore the color of that one, let it be what it may, 
and the white in the first marble, are hetera. Snow is white, snow and paper 
are hetej^i, therefore the color of snow and the color of paper are hetera, I. 
e., snow has a color and paper has a color and the two colors are hetera. 

The sixth and eleventh modes, which are similar in substance, contain 
greater difficulties. When we say this apple is sweet, that pear tastes like 
this apple, it is quite clear that the conclusion, therefore, that pear is sweet, 
follows from the premises, though this conclusion is an homonical proposi- 
tion. The taste of this apple and sweet are homon, the taste of this apple 
and that of that pear are similia, therefore the sweet in the apple and the 
taste in the pear are similia; but similia have a common name, and therefore 
the taste in the pear when named, is called sweet, and we say in the conclu- 
sion, that the pear is sweet, i. e., that the taste of the pear and sweet are 
homon. Now if we examine the above syllogism closely, we will see, that in 
the premises there are subjectively four heterical existences, to-wit; 1st, The 
taste of this apple; 2nd, Sweet; 3d, The taste of this apple; and 4th, The taste 
of that pear ; three ot which subjective existences are objectively homon. 
The taste of that pear only, is located in an heterical where with reference 
to the where occupied by u The taste of this apple, sweet, and the taste of this 
apple;" the other three heterical existences of the premises subjectively; but 
objectly these three are homon. But the sweet mentioned in the conclusion 
is not objectively homonical with the sweet in the first premise, they are ob- 
jectively similia, and because they are similia they have a common name 
and we say This pear is sweet, i. e., one of the gregaria of this pear and 
sweet are homon. Therefore in modes 6th and 11th there are but two objec- 
ive existences in the premises, which are inter se similia, and in the conclu- 
sion, one of these similia appears located in one of the objective wheres 
mentioned in one of the premises, as the other one of the similia was located 
in the other where in the other premise. In mode first we saw that of the 
four subjective existences in the premises, the two in the first premise were 
homon, and the two in the second premise were homon; in modes 6th and 
11th, the two subjective existences in one premise and one of the subjective 
existences in the other premise, are objectively homon. A.nd we must see 
hat it we take the conclusion, The sweet in this apple and the taste in that 
pear are similia; and dress it in common language, viz: That pear is sweet, 



86 
and then combine this conclusion with the homonical proposition "of the 
above premises, and we w T ill be in mode first, and will gain the other premise 
of the above syllogism as the conclusion: The taste of this apple is sweet the 
taste of that pear is sweet, therefore the tastes of the pear and apple are 
similia. And to make the matter still clearer, we may suppose three persons 
whom we will call A, B and C, to be sitting in a room with two apples in their 
hands. A tastes both of the apples and says secretly to himself, "this apple 
is sweet and that apple is sweet," and then drawing the conclusion in mode 
1st, he says aloud, "this apple tastes like that one;" B then tastes one of the 
apples and says, "this apple is sweet;" well then says C from what A and B 
say, "the other apple is sweet also." 

But hitherto we have not used what are called universal propositions 
for either of our premises, and when general propositions are used in mode 
1st, it is then, that a petitio principii is supposed to occur. We did not dis- 
cuss this matter when treating of mode 1st, for the reason, that we desired 
to get the reader further along in the knowledge of some of the other modes^ 
so that he might be better prepared for such discussion. When we say, all 
men are mortal, Socrates is a man, and, therefore Socrates is mortal, it is said 
that the conclusion, Socrates is mortal is implyed in the first premise, All men 
are mortal. The difficulty in this syllogism is, indeed somewhat below the 
surface, but if we set clearly before us the existences, which are really com- 
pared in the premises, the solution will be more easily obtained. All men 
are mortal, or its equivalent, Man is mortal, shows that one of the capacial 
gregaria sine qua non of man and mortality are homon; Socrates is a (one) 
man, shows that the existence called Socrates and one. of the existences 
called man are homon; and therefore Socrates, who is homonical with one 
man, and other men aresimiiia, in mode 1st. The simile, mortality, exists in 
every object, which may be called man, bat Socrates, i. e., the object designa- 
ted by that name, may be called a man, and therefore this simile exists in So- 
crates; for man is the common name of similia. In the foregoing syllogism 
let us write the premises and conclusion thus: Socrates and a man are ho- 
mon. One of the gregaria sine qua non of man and mortality are homon, 
Therefore the gregaria sine qua non of man and the gregaria of Socrates are 
similia, and One of these gregaria of Socrates then must be mortality, Socrates 
must be mortal. 

Suppose we look back to what we have called nominal truths, where 
we saw that when an object of vision arose into conciousness we called it 
color, to distinguish it from conscious truths of the other senses; and sup- 
pose that the first object of vision should have been the color, which we now 
call red; red then would have been called color' to distinguish it from con- 
scious truths of the other senses. Then suppose green to have arisen into 
consciousness, green too would have been called color, to distinguisn it from 



87 
objects of the other senses, and then red and green, as color, as distinguished 
from objects of the other senses, are inter se similia, and therefore each of 
them is a color. Now, if we collect into an homonical proposition the very- 
thing, which enables us to differentiate objects from other things into colors, 
to- wit, visibility, we will say, All colors are visible, or its equivalent, Color is 
visible, i. e., Color and visibility are objectively homon, and if we then add 
That red is a color, i. e., Red and one color are homon, it will follow that the 
object called red and visibility are similia i. e., red as an object distinguished 
from conscious truths of the other senses is distinguished in the same man- 
ner as other colors, to-wit, by being visible. And we must perceive that the 
first premise gives visibility as the ground of differentiation from the con- 
scious truths of the other senses, the whole of which ground lies partly in 
the visual faculties and partly in external objects, that is, in the relation of 
these, and it gives also color as the name to distinguish that part of the 
ground lying in external objects; and hence color and visibility are objective- 
ly homon. The second premise takes one of the subjective similia so diff- 
erentiated, and pronounces this similie andRED, a color further distinguished 
among colors to be homon; and hence this simile and any other simile are 
similia (non simile est idem) and red as a color and visibility, when located 
in the same where, are homon, for similia have a common name and when 
their wheres are homonical, they are objectively homon. 

Again, suppose we take several sticks, each one of which we dot with 
differently colored dots in such manner that by looking at the sticks when 
thus dotted, we cannot by the dots discriminate one stick from another, and 
suppose that each dot on any stick can be discriminated from any one of the 
other dots one the same stick, and to distinguish the dots inter se, we call 
one a, another b, c, d, &c. Now letting the dots in the aggregate be the very 
things, which distinguish the sticks before us from other things, we will call 
these dots, in the aggregate, in fasceculo, A. But supposing thai by the 
lengths of the stieks we are able to distin°;ish the sticks inter se, we will 
call a particular stick B, another C and another D. Now we can say that 
one of the dots of every A is a, i. e., one of the dots of any A and a are ho- 
mon. But B, this particular stick, which I now hold in my hand and men- 
tion by the name B, is a (one) thing, whose aggregate dots are called A, i. e. 
B and one ot the A's are homon, therefore any one of the A's excepting the A 
which I hold in my hand and mention by the uame B, and the A which I 
hold in may hand and which is the same thing as B, are similia; and hence 
the homonical a which we find in any A excepting the A, which is also B 
has a simile, a dot like itself, in the A in my hand which I may call also B* 
B is a. 

It must be confessed that the exposition of this matter is some what 
difficult; and heretofore all logicians have failed to understand the true state 



he 



88 
cf the case, but by thinking over the matter for several times, we hope the 
reader will be able to see through it. Perhaps it will appear more clear to 
some minds, if we dismiss differential terms for the aggregate existance, and 
distinguish them merely as hetera; then one of the gregaria sine qua non of 
1st object and mortality are homon; let this be our first premise. And then 
it must appear that if we say a second object and the 1st are similia, it will 
follow in mode 6th, that the simile mortality located in the first objects has a 
simile located in the second one and this simile is mortality. But if after 
the first premise, we say that the 2d object is one of the first kind of objects, 
this proposition, though homonical, is quasi similical, and the conclusion 
tromthe homonical premises that the gregarium mortality located in the 1st 
object has a simile in the second one is quite evident, and this simile located 
in the second object must be called by the common name, mortality, and 
hence one of the gregaria of 2d object and mortality are homon. All men 
are mortal, 1. e , one of the respects in which men are similia and mortality 
are homon; Socrates is a man, i. e., Tne object called Socrates and one of the 
similia named man are homon; therefore the respect, to-wit, mortality, in 
which men are similia and which is a gregarium in other men, and this res- 
pect in the object called Socrates, since he is a man — Socrates is mortal. 

The reason that syllogism, like the above are so difficult to understand, 
is that we lose sight of the wheres in which the respects, the gregaria, 
which render objects similia, exist. When we say, Snow is white, the snow 
in which this gregarium white, exists, or did exist, has or had an objective 
where, but this where is indefinite and undistiuguishecl in our minds from 
other wheres. But when we announce to a friend in the street that Snow is 
white and then add that an object in our house, which object the friend has 
never seen nor heard of before, is snow, he will immediately conclude that the 
colors of the object in our house and of the snow located in an indefinite where 
are similia, and therefore he would say that the object in our house is white. 

Now we do not concede that this argument is a petitio principii, that 
whea we say all snow is white, we imply that the object in the house is white; 
before this conclusion can be reached, without seeing the object itself, we 
must first learn that the object in the house and snow in the respect of color, 
are similia, and this we do when we are informed that the object in the house 
and one of the similia named snow are homon. So when we say all men 
are mortal, we do not imply anything respecting the object named Socrates, 
for Socrates may be the name of a statue or of a fictitious god like Jupeter. 
In the syllogism, all men are mortal, Socrates is a man, and therefore So- 
crates is mortal, however, both premises us they are usually unnerstood, and 
the conclusion, are false. Iron already fused is Dot fusible unless it he first 
congealed again ; neither are dead men mortal, requiem eternam Domine da eis. 

In the sillogism, All men are mortal, All kings are men, therefore all 



89 
kings are mortal; mortality is one of the gregaria sine qua non of man, and 
man is a sine qua non of a king, and therefore mortality is a sine qua non of 
kings. It may be said, indeed, that when we say All iron is fusible; so soon 
as we say of any object tnat it is iron, we have already ia the first premise 
asserted that it is fusible, and it is true thai by the combination of the prem- 
ises we reach the conclusion: and this is the case in every syllogism, whether 
either of the premises be a universal proposition or not. When we speak of 
particular objects and say A and B are similia, so soon as we say A and C 
are similia, we bring B and C to be similia, yet there is no petitio principii 
about it. 

Now when we say Man is mortal, we mean that one «f the gregaria 
sine qua non of man and mortality, are homon: but when we say Man is a 
mortal, we mean that each man and one of the similia, each one of which is 
named a mortal or mortal being, are homon: and this proposition brings 
man among the similia called mortals, in each one of which there exists the 
simile— mortality. We have perhaps gone far enough with the explanation 
of this matter. 

Modes 7th and 14th are very easily understood: Sugar is sweet — 
homon; No vinegar is sweet, or Yineg'ar is not sweet — differentia; There- 
fore the tastes of sugar and vinegar are differentia. The 9th and 12th modes 
are easy: and after having gone through the previous explanations, we do 
not deem it necessary to consider the remaining modes, as the principle of 
each of them has already been exhibited in some of the foregoing explan- 
ations. It may, however, be well enough, in order that the reader may have 
a clear understanding of our system, to take a view of those rules which 
writers generally have laid down for the regulation of the syllogism. 

And in order that the reader may better understand the whole matter, 
it must be observed that logicians have divided propositions into universal 
affirmative, as All men are mortal, which class of propositions they distin- 
guish by the symbol A; universal negative marked E, as No gold is green; 
particular affirmative marked I, as Some islands are fertile; and particular 
negative marked O, as Some men are not black. And with these four classes 
of propositions they commence to syllogize and to construct rules for obtain- 
ing true conclusions. 

And the first rule which they give, is that Every legitimate syllogism 
must have three and only three terms — the middle and the two terms of the 
conclusion. Although this rulej if we look merely at terms, be true, yet we 
consider logic to be concerned about more than terms, and therefore, we state 
instead of this rule that In every legitimate syllogism, there must be four and 
only four subjectively heterical existences in the premises, two of which — one 
in each premise — must be objectively hetera, and the two of which with 
which the other two are each compared, must be objectively homon, or 
similia or commensura inter se. 



90 

The second rule which they give, is that Every legitimate syllogism must 
have three and only three propositions: in this we are agreed. 

The third rule which they give, is that The middle term must not be 
ambiguous. This clanger is sufficiently guarded against by our first rule re- 
specting every legitimate syllogism. 

The fourth rule which they give, is that The middle term must be dis- 
tributed once at least in the premises by being the subject of an universal 
affirmative or the predicate of an universal negative proposition. For, say 
they, if we say white is a color, black is a color, in which propositions the 
middle term — a color — is not distributed, we will conclude falsly that black 
is white. But after what we have said heretofore, we think, it will readily 
be perceived that both of the above premises are homonical propositions an$ 
that the predicates of each — a color — are objectively two and not one and the 
same existence, they are not liomon, and thai these two existences have been 
differentiated from existences of the other senses, into colors, in which class 
of existences as distinguished from other things, as nominal truths, they 
are similia, the name color will distinguish either of them from existences of 
the other senses. When therefore we say, white is a color, black is a color, 
it does not follow that white is black, but that white and black as distin- 
guished, not inter se, but from other things are similia. White is a color, 
black is a color, therefore white and black, as nominal truths, are similia. 
But it does not follow that inter se, white and black are similia, unless it. ap- 
pear that the predicate, a color in the first premise, and the predicate, a 
color in the second premise are inter se liomon, or similia; the middle 
term therefore is faulty, not because it is not distributed, but because two 
existences are used which do not appear to be inter se similia. The fourth 
rule, therefore, laid down by writers, as a guide to keep us upon the true 
process of the mind in syllogising correctly, w T e. conceive to be, not only of 
no value, but erroneous. 

The fifth rule given, is that Wo term must be distributed in the con- 
clusion, which was not distributed in one of the premises. "All quadru- 
peds are animals, a bird is not a quadruped, and therefore a bird is not an 
animal." This conclusion is evidently erroneous; and it is quite clear that 
those, who were engaged in the construction of this rule, saw, independently 
of the syllogistic process in the premises, the error in the conclusion, which 
from the appearance of the words in the premises might be supposed to fol- 
low legitimately. The proposition, "All quadrupeds are animals." means 
simply that each quadruped and one animal are homon, and when we add 
that a bird is not a quadruped, i. e., that each bird and any quadruped are 
differentia, it does not follow that each bird and any auimal are differentia* 
what follows legitimately, is that each bird and the animals homonical or 
similical with the animals included in the predicate of the homonical pro- 






91 

position "all quadrupeds are animals" are differentia. For bird and animal 
are brought into the comparison in the conclusion by means of an homonical 
existence or similical existences, with which they were each of them com- 
pared in the premises. We stated in our first rule that each existence, which 
appears in the conclusion, must be compared in the premises with the same 
middle existence or with two existences inter se similia or commensura. 
And in the obove premises quadruped is compared with one animal, and 
quadrupeds being inter se similia, bird is then compared with one of these 
similia, and the conclusion must be that the animal compared in the homoni- 
cal proposition and found to be one of the quadrupeds and every bird must 
be cliffirentia, but nothing can be infered respecting any other animal, except 
it be a simile, than the animal spoken of in the first premise, which was 
homonical with quadruped. Red is a color, Green is not fed, are premises 
just like the former, and from them it follows that the one color homonical 
with red and green are differentia. The fifth rule therefore is of no value 
in our system, it is erroneous and falacious as a grade in the syllogistic process. 

The sixth rule given, is that From negative premises you can infer 
nothing. This rule in our system has no meaning, for, we do not admit that 
there is any such thing as an independent negative proposition. But calling 
such propositions, wdiich have no, none and not in their negative, the 
rule itself is not true, it is only true that we can not infer a categorical con- 
clusion. From the premises "A fish is not a quadruped, A bird is not a 
quadruped," it legitimately follows that a fish and a bird are differentia or 
similia (mode 4th). 

The seventh rule given is that if one premise be negative the conclu- 
sion must be negative. This rule in our system means nothing. 

Now in stating every homonical proposition, such as All men are mor- 
tal, we must be careful to see whither the predicate be one of the gregaria of 
the subject or not; for if it be not, and it be represented b} 7 an adjective name 
in order to make the proposition clear, some noun must be placed after it, or 
understood for adjective names which are not the representatives of grega- 
ria, are the names of existences standing as a class by themselves. When we 
say "All gold is precious," we mean that all gold and one of the things es- 
teemed of value among men, are homon; the proposition therefore should be 
stated tins; All gold is a precious thing, and then we can add that All 
gold is a mineral, and it will follow that the mineral homonical with gold is 
a precious thing. Mr. Hamilton gives as the second rule, that "The subsump- 
tion must be affirmative," and he illustrates this rule by the following ex- 
ample; "All colors are physical phenomena, no sound is a physical phenome- 
na;" "Here" says he, "the negative conclusion is false, but the affirmative, 
which w T ould be true — all sounds are plrvsical phenomena— can not be in- 
ferred from the premises, and therefore no inference is competent at all." 



92 

(page 289 ) After what we haye said heretofore, I think, it will be very easy 
to see through Hamilton's mistake. When we say that "All colors are physi- 
cal phenomena," we mean that each color is a (one) physical phenomenon, 
and when we add, No sound is a color, we mean that any sound and any color 
are differentia, and therefore we can infer, not that no sound is a physical 
phenomena, but that all physical phenomena homonical with colors and 
sounds are differentia. We have gone far enough perhaps, in this direction 
to make ourselves understood 03^ the reader. 

Before leaving this chapter, however, it seems necessary, t'lat w T e 
should make some remarks tending in another direction. It is the uni- 
mous doctrine of logicians hitherto, that one of the premises at least must be 
what they call a universal proposition, otherwise no legitimate conclusion 
can be drawn. And hence, if we should take a stick and apply it to a table 
and find the lengths of the stick and table so be commensura'and then apply 
the stick to another table and find the stick to be longer than it, and we should 
then make the following statement; lsttable=stick, 2d table<stick, therefore 
1st table > 2d table, this would not according to the received doctrine be a 
legitimate syllogism. But if this be not a legitimate syllogism, what is it? 
General propositions are necessary at all to enable us to syllogise, excepting 
A'hen we wish to syllogise with gregaria or a grcgarium sine qua non of ob- 
jects. When we say all A is b, i. e., one of the gregaria sine qua non of A 
and b are homon, no B is b, i. e., the gregaria sine qua non of B and b are 
differentia, it follows that A and B are differentia. In such cases as these, 
general propositions are necessary; but such cases from but a part of the in- 
stances, in which the syllogistic process is used. And from the consideration 
no doubt, that general propositions are always necessary in order to be able 
to syllogise, J. Stuart Mill, concluded that the syllogistic process was not 
realy inferential reasoning. He says "In the above observations it has, I 
think, been clearly shown, that, although there is always a process of reason- 
ing or inference, where a syllogism is used, the syllogism is not a correct 
analysis of that process of reasoning or inference; which is, on the con' ary, 
(where not a mere inference from testimony) an inference from particulars to 
particulars: authorized by a previous inference from particulars to generals 
and substantially the same with it; of the nature, therefore, of induction." 
Now when we tell a friend that the heighth of a stove in this room is com- 
mensural with the heighth of a stove in the other room, which latter stove 
the friend has never seen, and that the heighth of this stove is three feet, and 
then ask him from these data to tell us the heighth of the stove in the other 
room, if he does not ayllegise and on the syllogistic process make an infer- 
ence, I should like to know in what other manner, by what kind of induction, 
lie would be able to solve the problem. 



98 



CHAPTER, XIX. 

EXPLANATION OF SYLLOGISM CONTINUED. 

Having explained the syllogism, in which the first four classes of pro- 
positions are combined, we come now to give some further consideration to 
the syllogism combining the first and second anct fifth and sixth classes of 
propositions. And of the manner, in which the first and second classes of 
propositions are combined in the syllogism, we have already said sufficient; 
it is to the manner of combining commensural and incommensural proposi- 
tions, therefore, that we will more especially direct the attention of the reader. 
In our explanation of propositions heretofore, we observed that, similical 
and differential propositions spring from homonical propositions; we showed 
this to be the case also with commensural and incommensural propositions. 
Homon is at t)ie bottom of ail propositions; hetera are at the bottom of all 
knowledge; and the power of the mind t<o heterate depeuds upon time and 
space. We must also perceive that, homonical propositions, which are col- 
lected into heterical, similical, differential, commensural or incommensural 
ones, must in every instance have a local reference in the subject or predicate; 
tor, in every proposition there is a comparison between two existences, and 
if these two existences be considered merely heterically, they can not sub- 
jectively be homon; to be homon the subjective •hetera must be located in an 
homonical where at an homonical time. We have already seen, how we 
come to have the knowledge of existence; and after this has been obtained, 
we may say indeed, that this grounded in the ego and one existence grounded 
in the ego are homon; but when the one existence is grounded in the ego, 
it is located there in the same where with this, and at an homonical time; 
and the on,e existence and the this referedto must also, irrespective of time 
and space, be subjectively similia, otherwise the bringing them into au ho- 
monical where at an homonical time will not make them homon. An object 
•may be heard by the ear aud another seen hj the eye; irrespective of time 
and space they are differentia, and although they may subjectively be located 
in the same where at an homonical time they do not become homon. And 
where we say, This is an existence, aud then again, That is an existence, the 
first existance and the second one are hetera, and if they can not be discrimi- 
nated further they are similia. Existences, however, is a name, which does 
not distinguish existences inter se. But if we say, This is white, and then 
again, That is white, as white is a name, which distinguishes existences inter 
se, if the first thing and the second thing be not similia, in the respect of 
color the word, white has been misapplied to one or both of ihem. 



94 

Now in commensural and in in coin men sura] propositions, the things 
compared are always similia, yet commensural and incommensural propo- 
sitions are not derived from similia but from homon. If we take a certain 
stick and say, the length of this stick is one (the unit) i. e., the length of this 
stick and one are homon, and we then go to an ©ther stick and say, the 
length of this stick and one are homon, if the lengths of the two sticks be 
not commensura, one has no definite meaning; and we can give a definite 
meaning to one only by taking some honionical thing as the unit of meas- 
urement. If then we make the length of a particular stick the homonical 
thing by which to define one, and apply this length to another stick, and we 
can not discriminate the lengths of the two, we may say, the length of the 
first stick, the homonical thing which we have made the unit of measure- 
ment, and one are homon, and as the length of the second stick when com- 
pared with the first cannot be discriminated from it, we must from a mental 
necessity call it one also. The length ot. the first stick and one are homon, 
the length of first stick and that of the second are commensura, therefore the 
length of second stick and one are commensura; but commensura must oi 
necessity have a common name, and hence the length of second stick must 
be called one, and length of second stick when not compared with another, 
and one are homon. And if we combine this proposition, with the homoni- 
cal one which gave the unit of measurement, we will have length of first 
stick and one are homon, length of second etick and one are homon, there- 
fore lengths of first and second sticks are commensura, since one and one 
(not twice one) are commensura, 1=1; and hence the length of any stick 
which may be called one, will be commensural with the first stick. If how- 
ever, the length of first object<2d and 2d<3d, then lst<3d, and we hare 
three heterical objects, which are inter se incommensura, and we may con- 
tinue by sorites, 3d<4th, therefore lst<4th, but 4th<5th, therefore 1st < 5th, 
but 5th<6th, therefore lst<6th, ana therefore 1st or any of one of the objects 
after 1st, is less than 6th, and so on. Here then we have six objects inter se 
incommensura, and as they are similia in kind, each of them in a like man- 
ner, has been differentiated from other things, and they have a common name 
distinguishing them trom other things in kind; but this name does not dis- 
tinguish them inter se. And if we name them 1st, 2d, 3d, &c, these distin- 
guishing: terms merely distinguish them heterically inter se, but they do not 
show the incommensural relations existing among them, and therefore by 
the use of such terms, we can not show any results further than heterical, 
which we may hare obtained by comparing those objects inter se. There is 
therefore, only one possible way for us to form a language by whase terms, 
we may be able to show the results of the minds comparisons among com- 
mensural and incommensural objects. After that we have gained the knowl- 
edge of the homonical thing, which we establish, as the unit of measurement 



95 

in an homonical proposition, we may apply this homonical unit to a second 
object, and if the homonical thing be measured just twice upon the second 
object, we may arbitrarily name twice one, two, and then twice one and two 
will always be in our minds commensura, and two will show the resnlt of 
the comparison between any object named two, and the homonical thing 
called one. And by naming thrice one, three, four times one, four, and so 
on, we will hare the cardinal numbers applied to similia. One, then, will be 
a common name for all objects, which are inter se similia and inter se com- 
mensura; and so also will 2, 3, 4, &c. But 1, 2, 3, 4, &c, distinguish incom- 
mensura inter se, and show by the relations of the homon inter hetera, the 
incommensural relations existing among siniiiia. And these arbitrary signs 
of commensural and incommensural relations may be applied to any similia 
in nature, by taking an homonical simile as the unit of measurement; they 
may be applied to lengths, to heats, to colds, to weights, to volumes &c. It is 
the peculiar perogative of mathematics to develop and carry out these 
principles. 

But we must see that the unit of measurement, in all cases, is the pre- 
dicate of an homonical proposition, and then commence commensural and 
incommensural propositions. And the syllogism with commensural and in- 
commensural propositions, is used in every branch of mathematics from the 
beginning to the end. And as the demonstrations, in mathematics depend 
upon definitions, it is necessary to consider the manner in which we syllo- 
gise upon those definitions. We have, heretofore said, that all definitions, 
which state directly what a thing is, are contained in homonical propositions ; 
this is the case in mathematics, and as geometry affords us sufficient illustra- 
tion of our subject, we will confine our remarks to it. Geometry, it needs 
not to be shown here, treats of relations in space, aud hence a point is a 
position, a where in space, i. e., a mathematical point and a where in space 
are homon. A line is the cause of consecutive points in space. A straight 
line is the course of consecutive points in a uniform direction in space, i. e. 
a straight line and a course of consecutive points in a uniform direction in 
space are homon. And again, the portion of space included between two 
lines touching each other at a given point, and an angle are homon. Again, 
the portion of space, which being included by two straight lines touching at 
a given point, which point being taken as a center and a circle described, is 
a quadrant of the circle, and aright angle are homon, and so on. All the 
foregoing definitions, and all of the direct definitions upon which in geometry 
demonstrations are constructed, are contained in homonical propositions. 
But when we say, an acute angle is an angle less than a right augle, we do 
not directly define an acute angle, and therefore the proposition is an incom- 
mensural one, and so also when we say, an obtuse angle is greater than a 
right angle, And it mu3t be observed that line is a common name for simi- 



96 
lia and that straight line is also a common name for similia, line being a 
genus of which straight line is a species ; and so also with angles &c. 
But alter the definitions in geometry, then iollow what are called 
axioms. These axioms are contained in commensural and in incommensural 
propositions, the bottom of which, as we have seen, is homon. But the corn- 
mensural and incommensural propositions which contain axioms are founded 
more immediately upon the Syllogism. The axiom, that Things inter se 
similia, which are equal to the same thing are equal to each other; is obvi- 
ously the condensation of a syllogism into a commensural proposition. Let 
the length oi a certain stick be the homonical unit of measurement and call 
. this length one; one then will be a common name for all lengths commen- 
sural with that of the stick, Now if we apply this stick to another, which 
we, will call A, and they be found to be commensura, we will say, A and 1 are 
commensura, A=l; and if then we apply the first stick to a third one which 
we will call B, and find them to be commensura, we will say, B and 1 are 
commensura, B=l; then we have the syllogism A=l, B=l, therefore A~B. 
And-all the axioms of geometry are founded immediately upon the syllo- 
gistic process, though homon is at the bottom of the whole thing. If equals 
be added to, equals, the. sums will be equal; is very plainly founded on the 
syllogism. If A— B, as they are commensura, we may call each of them — 
three; and is -A'=;B', as they are commensura, we may call each of them— 
two; then if we apply the homonieal unit of measurement to xi, we find that 
thrice one and A are commensura and so also of B; and if we apply the 
unit to. A', we find that twice one and A' are commensura and^s© also with 
B' .; then A-fA..' must be equal to five times one, or five, and .3-^-3'= Rye 
times ©ne, or five; and we have the syllogism, A-fA' =5, B-f-B'=5, therefore 
A-fA.' =rB-j-B\ So also when we say that magnitudes, which being applied 
to each other coincide throughout their whole extent, are equal, this axiom is 
founded upon the syllogism : and in this case we come closer to the homon 
at the bottom. Suppose we have before us a certain object called A, and an- 
other called B ; if now we represent the magnitude of A by A,. and that of 
B by b, we must then say, the magnitude of A and a are homon, and the mag" 
nitude of B and b are homon; but if a and b cannot be discriminated other- 
wise than heterically, if they coincide, they are commensura, a=b, and each 
of them may be called d, and we have m. of A=d, m. of B=d, therefore m. 
of A=m. of B, But if in the above case a and b can be incommensurated, 
we. would have m. of A and a are homon, m. of B and b are homon: but a<b 
therefore m. of A and a are homon, a<b, therefore in. of A<b; but m. of B 
and bare homon, m. of A<b, therefore m. of A<m. of B, which is the foun- 
dation of the axiom, that The whole is greater than any of its parts. For, 
let m. of the whole be represented by a, and the m. of any part be represented 
by b; then m. of the whole and a are -homon, m of part and b are homon, but 
b<a, therefore etc. 



97 

Now it may be said, that it is strange that axioms which are regarded 
as sufficient truths should after all, be arrived at by a process so difficult to 
understand. This however, is not strange at all, the mind runs this course, 
as it were, in a flash and perceives the truths expressed by axioms without 
much difficulty; though to trace this course' or process of the mind is very 
difficult. There are, however, gome of the elementary truths in geometry, 
regarded as axioms, which seem, at first, to be peculiar, and they have been 
called inductions; they are contained in such propositions as the following; 
"Two straight lines, which have two points in common cannot afterwards 
diverge," "Two straight lines cannot inclose a space," "Two straight lines in- 
tersecting each other cannot both ©f them be parallel to a third straight line," 
and so on; Such propositions, however are founded upon the syllogism. 
Take the proposition, Two straight lines having two points in common cannot 
afterwards diverge, or what is equivalent, Two straight lines having two points 
in common must coincide throughout their whole extent, Now a mere 
glance at the proposition will show us that it is grammatically in the poten- 
tial mode. And it must be evident that there are differential courses, i. e., 
that a straight course and a crooked one are differentia, and that two lines 
one of which runs a straight course and the other a crooked one, are in ca- 
pacity differentia.; given a certain number of points in space, a line that can 
run through all of the points, and a line, that can run through only some of 
them, are inter se differentia. 

A B C 



u 

Let, therefore, A B C, be a straight line and let a represent its uniform 
course from A to C; then a straight line and a are homon. But let A B D 
be another line, whose course from A to D is represented by b, then A B D 
and b are -homon. Then if a and b be homon, or similia, ABC and A B D 
will be similia. But the circumstance that- the point at D in b can be dis- 
criminated from any point in the course a, and that at A and B, a and b co- 
incide, shows that the courses a and b are differentia. Then the capacity of 
the line ABC, and a are homon, and the capacity of the line A B D and b 
are homon, but a and b are differentia; therefore we have, capacity of line A 
B C and a are homon, a and b are differentia, therefore, capacity of line A B 
C and b are differentia; but capacity of line ABD and b are homon, capacity 
of line ABC and b are differentia; therefore ABC and ABD are differentia; A 
B C however, by hypothesis, is a straight line, therefore A B D is not a 



98 
straight line. And from the foregoing demonstration, we can easily see, how 
the syllogism underlies the proposition that two straight lines cannot inclose 
a space ; for, a space inclosed is a space surrounded by consecutive points, 
and if we lay down one straight line, another straight line touching the first 
one in any two points, cannot diverge from it, but must coincide with it in its 
whole course; but a course, a mere uniform direction can inclose nothing. 

"We have gone, we hope, far enough, to show that the axioms of mathe- 
matics are founded upon the syllogism, and leaving the axioms, therefore, we 
will give one illustration of the principles of our system of reasoning from a 
simple proposition in geometry. Take the proposition that the sum of the 
angles of a triangle are equal to two right angles. 




Let D E C be the triangle and prolong the side DE to A; and from the 
point E draw EB parallel to DC, then from previous syllogisms we know 
that the angles ODE and BE A are commensura; we also that the angles CEB 
and DCE are commensura. But as CDE and BEA are commensura, we may 
call them by the common name A; and as CEB and DCE are commensura, 
we may call them by the common name B; Then either CDE or AEB is an 
A, and either CEB or DCE is a B; and we may call CED, C; then AB 
and C and the sum of the angles of the triangle are commensura. But the 
sum of all the angles that can be formed at a given point on one side of a 
straight line and two right angles are commensura, the angles A, B and C are 
the sum of the angles so formed at the point E, therefore A, B and C together, 
and two right angles are commensura. 

CHAPTER XX. 



Having explained in the previous chapters the manner in which the 
syllogistic process proceeds, we do not deem it necessary to elaborate much 
upon the Entymeme, Sorites or Delemma. When either one of the premises 
of a syllogism is expressed and the other understood, the expressed premise 
with the conclusion is callen an entymeme; as Iron will rust, therefore the 
plowshare will rust, or .The plowshare is iron, and therefore it will rust. In 
ouch cases, it is easy to supply the premise, which is understood. Any per- 



son, well grounded in the principles of the syllogism, will have no difficulty 
in managing the enthymeme. 

No\V when a conclusion has been legitimately drawn from premises, 
this conclusion may be made a premise and combined with either of the for- 
mer premises, and another conclusion may then be drawn; and then this lat- 
ter conclusion may be combined as a premise with the first and so on. 
When we continue to syllogize in this manner, the chain of syllogisms is 
called a Sorites; as, A and B are similia, B and (J are similia, therefore A and 
C are similia; but C and D are similia, therefore A and D are similia; but 
D and E are similia, etc. And this process may be pursued with any of the 
modes and figures, which we have given in the preceding paradigms. 
Thus: A and B are similia, B and C are differentia, therefore A and C are 
differentia; but C and D are similia, therefore A and D are differentia; but 
D and E are differentia, therefore A and E are differentia or similia etc. 
Now we stated in a previous chapter that there are five objective nominal 
truths, and if we let A stand for one of them, B for another and C, D and E 
for the others severally, we may syllogize upon them in the following man- 
ner : A and B are hetera, B and C are hetera, therefore A and C are hetera ; 
but C and D are hetera, therefore A and D are hetera; but D and E are 
hetera, therefore A and E are hetera; and therefore A, i. e., the thing distin- 
guished by the name A, and taste, or sound, or feeling, or color, or scent are 
homou. And this shows us the manner in which we come to use disjunctive 
propositions; they are conclusions of syllogisms. The sky is either clear or 
cloudy, why? There are two states, capacial gregaria, of the atmosphere, 
clistinguishad inter se by the names clear and cloudy; one of these states n*w 
exists, therefore it is either clear or cloudy, i. e., the present state of the at- 
mosphere and either clear or cloudy are homon. And when we say that Men 
are either black or white or ta-vny; this is a conclusional preposition drawn 
in the same manner as the one above: though there might be men of neither 
of tnese complexions, for aught we know. And in the conclusional propo- 
sition just given, that which is really affirmed is that one of the facial gre- 
garia of every man and one of the three colors namely, black, white or 
tawny, are similia. And as similia have the same name, the color of any 
man and black or white or tawny are homon. Again: Iron and glass are 
hetera, hetera are divided into two classes, namely, similia and differentia, 
therefore iron and glass are either similia or differentia. 

Now by the combination of disjunctive conclusional propositions in 
premises, we form the basis of what is called the Dilemma; thus, A and 
either B or C are similia, i. e., A and one of the two are similia, but either B 
or C, i. e., either one of them, and D are similia, therefore A and D are 
similia, therefore A and D are similia. And it must be noticed that there is 
an ambiguity in the use of the correllatives, either, or. In the first instance 



100 
A and either B or C are similia, we mean that A and one of the two are simi- 
lia, while A and the other may be differentiator aught that is disclosed by the 
proposition ; while in the latter instance, either B or C and D are similia, we 
mean that B and D are similia and also that C and D are similia. And it is 
this ambiguity in the use of the correllatives, that makes the dilemma kind 
of trap by which men are caught before they are aware of it. 

Now if we set down before us the propositions, A and either B or C 
are homon, but either B or C and D are homon, and be careful not to be mis- 
led by the ambiguity of the correllatives, we can easily see by considering 
these propositions how we come by such hypothetical enthymenes as the 
following; if A and B are homon, A and D are similia, and if A and C are 
homon, A and D are similia; but A and B or C are homon, therefore A and 
D are similia; (mode 1st). But taking again the two disjunctive propositions 
A and either B or C are homon, and D and either B or C are homon, and tak- 
ing the correllatives in both instances to mean one ot the two and not the 
other, we will have for conclusion that A and D are either similia or differen- 
tia. If A and B are homon, and D and B aie homon, A and D will be simi- 
lia; and if A and C are homon, and D and G are homon, A and D will be 
similia; but if A and C are homon and D and B are homon or A and B are 
homon and D and C are homon, A and D may be differentia. Again ; if we 
take the propositions A and either B or C are similia; E and neither B nor C 
are similia, it will follow that A and E are differentia. 

Now it is evident that we may take any categorical proposition and 
put into a hypothetical form. Take the proposition, Ice is cold, and we may 
say, If ice is cold; but from this latter expression, we expect some conclusion 
o follow, and we state the proposition in this hypothetical manner tor the 
purpose of drawing some conclusion, and therefore we give.it this illative 
wording. And in such cases we always take one of the premises of a syllo- 
gism and state it hypothetically. Take the syllogism, Rainy weather is wet 
weather, it is rainy weather, therefore it is wet weather; now we may state 
the second premise hypothetically, If it is rainy weather, and draw the con- 
clusion, It is wet weather, leaving the first premise unexpressed. We call 
such arguments hypothetical enthymemes ; and those expressions of argu- 
ment which have been commonly called hypothetical syllogisms, are merely 
hypothetical enthymemes stated first, and then throwing off the hypothesis, 
the enthymeme is stated again categorically, to show that the conclusion 
does not only follow logically, but also that the premises, from which the 
conclusion is drawn, are actual. Thus if A and B are similia then A and 
are similia; but A and B are similia, therefore A and are similia. In this 
example, the conclusion introduced by therefore does not at all depend 
upon the expression, if A and B are similia, then A and C are similia, but 
upon, A and B are similia and another premise understood. In, the syllo- 



101 
gism, A and B are similia, and B are similia, therefore A and C are simi- 
lia, any person, who looks at it, and grants thai C and B are similia, will 
readily go farther, and grant that, if A and B are similia, if such be really 
the case, then A and C are similia, and when you convince him that really A 
and B are similia, the hypothesis is thrown oft", and be acknowledges that A 
and C are similia. In such cases the conclusion is not drawn from the first 
hypothetical enthymeme — if A and B are similia then A and are similia, 
but from A and B are similia and the other premise, Band C are similia, un- 
derstood. If Socrates is virtuous, then he merits esteem; but Socrates is 
virtuous, therefore he merits esteem; why ? The virtuous merit esteem. So- 
crates is virtuous therefore he merits esteem. We du not consider it necessary 
t© go into an elaborate discussion upon such matter, we will, however, sub- 
jein a note. 

Note. — It is strange that neither Archbishops Whately nor Sir Wm. 
Hamilton were able to sound to the bottom of what they call hypothetical 
propositions, nor be able to perceive the true nature of the dilemma "A 
hypothetical proposition," says Whately, "is defined to be two -or more cate- 
goricals united by a copula (or conjunction) and the different kinds of hy- 
pothetical propositions are named from their respective conjunctions: viz; 
conditional disjunctive, causal &c." And again; k 'A conditional proposition 
has in it an illative force, i. e., it contains two and only two categorical pro- 
positions, whereof one results from the other (or follows from it)." And 
again, U A disjunctive proposition may consist of any mem be l of categ*ri- 
cals." That a proposition may be the subject of another proposition is very 
clear; as that John is a scholor, is not denied; but that one proposition may 
be a dozen propositions is certainly very strange. Sir Wm. Hamilton adopt- 
ing the explanation of Krug says (page 168) "Although, therefore, an hypothe- 
tical judgment appear double, and may be cut into two different judgments, 
it is nevertheless not a composite judgment. For it is realized through a 
simple act of thought, in which if and then, the antecedent and consequent 
are thought at once and as iuseperable. The proposition if B is, then A is, 
is tantamount to the proposition, A is through B. But this is as simple an act 
as if we categorically judged B is A, that is, B is under A. Of these two, 
neither the one — If the sun shines, — nor the other, — then it is day — if 
thought apart from the other, will constitute a judgment, but only the two in 
conjunction." Now the above is a misconception of the nature of proposi- 
tions, and it arises from the erroneous notions entertained by Hamilton and 
others respecting predication. Suppose in the above example given, we 
leave the if and then out, we will then have, the sun shines, it is day: Now 
Mr. Hamilton would admit that here are two propositions, but would answer 
that although there are two, yet it is not shown in any way ihat the one is 
connected or dependent upon the other without the words if and then. 
Very well; take the propositions A is B, C is B, A is C, and without the word 
therefore, before the last one, it is not shown by words, that this is the con- 
clusion of a syllogism. And if the words if and then possess the magic 
power to merge two propositions into one, we may use them also to merge a 
syllogism into a proposition, thus; if A is B and C is B then A is C, which 
accouling to Mr. Hamilton would be merely an hypothetical proposition. 
For when we say if A is B and C is B, we expect something to follow and 



102 

we perceive that A is C v does follow, and hence we may regard all this as but 
one continuous act of the mind. And respecting the expression tk if A is, 
then B is, or A is through B," this expression is not true in any case except- 
ing when A is the cause and always accompanied by the effect B Mr. Ham- 
ilton's erroneous notions of what he calls au hypothetical proposition led 
him to misunderstood entirely, what he calls an hypothetical syllogism. On 
page 246, following Esser, Hamilton says, a It however, an hypothetical pro- 
position involve only the thought of a single auteceedent and of a single 
consequent, it will follow that any hypothetical syllogism consists not of 
more than three, but of less than three capital notions; and, in a "rigorous 
sense, this is, actually the case. On this ground, some logicians of great 
acuteness have viewed the hypothetical syllogism ^s a syllogism of two terms 
and of two propositions. This is, however, erroneous; for in an hypothetical 
syllogism, there are virtually three terms. That under this form of reas- 
oning, a whole syllogism can be envolved out of not more than two capital 
notions, depends on this, that the two constituent notions of an hypothetical 
syllogism present a character in the sumption altogether different from what 
they exhibit in the subsumption and conclusion. In the sumption these no- 
tions stand bound together in the relation of reason and consequent, without 
however, any determination in regard to the reality or unreality of one or the 
other; if one be, the other is, is all that is enounced. In the subsumption, on 
the other hand, the existance or non-ex. stance of what one or the other of 
these notions comprises is expressly asserted, and thus the concept, expressly 
affirmed or expressly denied, manifestly obtains, in the subsumption, a wholly 
different significance from what it bore when only enounced as a condition 
of reality, or unreality, and in like manner, that notion which the subsump- 
tion left untouched, and concerning whose existence or non existence the 
conclusion decides, obtains a character altogether different in the end from 
what it presented in the beginning.'' This m explanation Hamilton obtained 
from, Esser. And hence from the above reasoning, if we suppose that we 
have before us a hat and a broom (which very supposition implys two sepa- 
rate existences) and we say, if the hat is not the broom, the hat and broom are 
are separate existences; but the hat is not the broom, therefore the two are 
separate existences, we make a sumption to get lit some vxktual third term, 
and this third term is envolved, because the terms in the sumption stand to- 
gether in the relation of reason and consequent, and in the subsumption they 
they are asserted to be realities, and hence the third term; then in the sub- 
sumption we take the sumption to be actual and real, and by this method of 
syllogising, we prove that the hat is not the broom, just as we supposed in 
the sumption. It is astonishing that a man of so great learning and natural 
ability as Hamilton should have been drawn into this subtle and trifling 
nonsense of the German. In what Hamilton calls Dilemmated judgments, 
he and Whatley are also in the dark., Hamilton says (on p. 170) "Dilemmatic 
judgments are those, in which a condition is found, both in the subject and 
in the predicate, and as thus a combination of an hypothetical form and of a 
disjunctive form, they may also appropriately be denominated Hypothetico- 
disjunctive. If x is A, it (x) is either B or — if an action be prohibited, it 
is prohibited either by natural or by positive law." * * * * * 
Now I apprehend, it will be impossible for any one to see why x is 
either B or 0, granting that x is A, without going through the process — A is 
either B or C, x is A, and therefore x is either B or C. Hamilton carries his 
errors respecting Dilemmatic propositions into what he calls Dilemmatic 
syllogisms; but we will not criticise further. 



108 



CHAPTER XXL 



THE SINGULAR HOMONICAL SYLLOGISM. 

Having treated of the Singular Syllogism and having explained pretty 

thoroughly the manner of the syllogistic process in the mind, it yet remains 

for us to show the further application of this process in the acquisition of 

knowledge. We have already shown that Irom the combination of two ho- 

monical propositions, as premises, we may gain similia or commensura in 

the conclusion. And if we represeut aggregate existences by B, C, D E &c, 

and any simple existence by A, we may then form an indefinite number ot 

homonical propositions, all ot which shall have A as the predicate, thus: 

j Gregarium of B and A are hoinon, 

Therefore similia '( [ lt . " C and A are homon. 

Therefore similia \ j u " D and A are homon, 

Therefore similia / \ M " E and A are homon, 

Therefore similia { tl u F and A are homon. 

And so on, which is a continued syllogism or Sorites. And a mere glance at 
the above chain of syllogisms will show us that, the simile A, exists in B, C, 
D, E, &c; and if B, C, D, E,&c, each points out an individual object, a swan, 
for instance, and A stand for white, tor instance, we would say that Swan B, 
Swan C, Swan E, and all Swans which we have seen, are white; they are all 
similia in this facial gregarium. Tills is generalization from experience. 
And by the aid ol conversation and books, we can of course, use the experience 
of others in the same manner as our own. And if from this experience we 
make a,a inference be} r ond experience, this process, which is wholy syllogistic 
within experience but no further, has been called by Bacon, "inductio per 
enumerationem simplicem, ubi non reperitur insiantia contradictoria.'* 

But if we return to the nominal truths spoken of at the beginning of 
our inquiries, any person will readily admit that all colors, not only those, 
which have been seen, but also those which can be seen, are visible, i. e., 
visibility and a sine qua non of colors are homon Color, however, is not an 
aggregate but a simple existence and therefore, not one of the gregaria of 
color, but. color itself and visibility are objectively homon, And au objective 
homon, however often its times can be heterated, is nevertheless always ho- 
mon; time in its modifications of past, present and future, cannot strengthen 
or weaken our belief in a homon. If I take a marble and inclose it in my 
hand for four hours, when I first put it into my hand I believe it to be an ho- 
monical thing, and at the end of four hours I nelieve it to be the homonical 
thing without dwnbt; the only thing, that can make me doubt of an objective 
homon, is that I do not always feel certain that in the course of time, the 
homonical thing may not have been removed and a simile have been put" into 
its place. The heteration of an objects times can have no heterating effect 
upon the object itself. The power of the mind to heterale, indeed, depends 






104 

upon time and space; but respecting the ego per se and the nop ego per se, 
homon is homon irrespective of time. And hence if we take an object as 
time can have no heterating effect upon it, a thousand years from to-day, it 
will be homon; and although time has been personified and endowed with 
capacial gregaria by the poets, it must be evident that time per se has noth- 
ing in it, to produce any effect upon the ego or non-ego. But as time has no 
capacity to heterate or differentiate objects, if we affirm that this where is a 
where of pure space, i. e., this where and one where or pure space are homon, 
and that where and a where of pure space are homon, it must follow that this 
where and that where are similia. If time per se can neither heterate nor 
differentiate, any two wheres of pure space are now, always have been, and 
always will be, Similia, so long as pure space and pure space are homon ; and 
so also with every other object so far as tim'e per se is concerned. 

But we may ask ourselves, has space any capacial gregaria to affect 
objects occupying it? And by the artificial production of a vacumm, we 
are able to decide upon reflection that here, in this instance, is a space, which 
has no capacity to interfere in any manner with objects occupying it, were 
any object in it. But if homon is homon, if space is space, this particular 
vacuated space ana* any other where of pure space are similia, they cannot be 
differentia, and hence no space can heterate, differentiate or incommensurate 
objects occupying it. We have therefore eliminated time and space, as agents, 
from our consideration; but before proceeding farther, we must explain some 
terms, which we will have occasion to use hereafter. 

If we take any homon, this homon to-day, will be homon a thousand 
years hence, so far as time and space are concerned, we will, therefore, call 
this homon an homonical homon. But if we take another homon, a like 
case will be with it, and to distinguish the second homon from the first, we 
will call it an heterical homon ; an homonical homon and an heterieal homon 
will then be hetera. 

Again; If the homonical homon and the heterical homon be inter se 

similia, we may call the heterical homon with reference to the homonical 

homon, a similical homon. An homonical homon and a similical homon 
will then be similia. 

Again; If the homonical homon and the heterical homon be inter se 
differentia, we may call the heterical homon with reference to the homonical 
homon, a differential homon. An homonical homon and a differential homon 
will then be differentia. 

Again; If the homonical homon and the heterical homon be commen- 
sura, we may call the heterical homon a commensural homon. An homoni- 
cal homon and a commensural homon will then be commensura. 

But again; If the homonical homon and the heterical homon be in- 
commensura, we may call the heterical homon, an incommensural homon. 
An homonical homon and an incommensural homon will then be in- 
commensura. 



105 
The following list will show the terms and the manner in which they 

distinguish objects: 

., , Homonical homon- a / il'^'Vi 
1st. TT -11 r homon. 

Homonical homon — a 



„ , Homonical h©mon— a [ } _ fprM 

M ' Heterical homon-b f heleltL 

QA Homonical homon — a ) c . .,. 

3d Similical homon-a' \^ H ; 

4th. ^»M J 1 ""! 1 Uiff -remit 



Differential homon 



ij[difF 



K4l Homonical homon — 2 ) 

oth - Commensural homon- fe' \ commensura. 

«., Homonical homon — 2 ) . 

6th - Incoiuuiensural homon-3 f """mmensura. 

Now with the above terms, the following syllogisms' which we call 

singular homonical syllogisms, because one premise at least in each mode is 

homonical, may be constructed: 

mode 1st. 

The homonical homon a, in the place — b to-day, and the homonical 
homon— a, in any where a thousand years hence, are homon. 

The homonical homon — a', in the place— c to-day, and the homonical 
homon — a', a thousand y^ars hence in any where are homon. 

Therefore the homonical homon — a, in any where a thousand years 
hence, and the homonical homon a', in any where a thousand years hence, 
aie si m ilia, 

MODE 2D. 

The homonical homon— a, in the where b, to-day, and the homonical 
homon — a, in any where a thousand years hence, are homon. 

The homonical liomon — a, in the where, b to-day, and the heterical 
homon c, in the where — d to-day, are hetera. 

Therefore the homonical homon — a, in any where a thousand years 
hence, and the heterical homon c, in any where a thousand years hence, 
are hetera. 

mode 3d. 

The homonical homon a in the where b to-day, and the homonical ho- 
mon a in any where, a thousand years hence are homon. 

The homonical homon a ia the where b to-day, and the similical ho- 
mon a' in the where c to clay are similia. 

Therefore, the homonical homon a in any where a thousand years 
hence, and the similical homon a' in any where a thousand years hence, are 
similia, f 

mode 4th. 

The homonical homon A in the where b to-day, and the homonical 
homon a in any where a thousand years hence are homon. 



tial 



106 

The homonical homon a in the where b to-day, and the differential 
homon c in the where d to-day are differentia. 

Therefore the homon ical homon a in any where a thousand years 

hence, and the differential homon c in any where a thousand years hence are 

differentia. 

mode 5th. 

The homonical homon a in the where b to-day, and the homonical ho- 
mon A in any where a thousand years hence are homon. 

The nomonical homon a in the where b to-day and the commensuraj, 
homon a' in the where c to-day, are commensura. 

Therefore the homonical homon a in any where a thousand years hence 

and the commensural homon a' in anj r where a thousand years hence are 

commensura. 

mode 6th. 

The homonical homon a in tae where b to day and the homonical 
homon A in any where a thousand years hence are homon. 

The homonical homon a in the where to-day and the incommensural 
homon c in the where d to-day, are incommensura. 

Therefore, the homonical homon a in any where a thousand years 
hence, and the incommensural homon c in any where a thousand years hence, 
are incommensura. 

After a careful study of the above mode in the singular homonical 
syllogism, the following reasoning, we believe, will appear obvious. If we 
let a homon, always be homon in our minds, and we make this homon a 
simile, i. e., it the homon a in the where b, have a simile in the where c, and 
another in the where d and so on, each one of these similia must have a com- 
mon name, and no matter if their heterical number be infinite and the points 
of time of some be in the past, of others in the present, and of still others in 
the future, yet we have no hesitation in believing that each one must be an A, 
for if it should not be so, homon would not be homon ; and that the really 
same thing should not be the same thing is absurd and impossible. But the 
homon in our minds has a simile in the minds of other men, and hence we 
believe without a doubt that two beings like ourselves a thousand years hence 
all colors, which they will know any thing about, will be visible, i. e., color 
and visibility will be to them homon. The same thing is the same thing, 
homon is homon, no matter about the modifications of time and space. Color 
and visibility are homon, visibility and visibility are homon. Therefore, 
color and visibility are similia (mode 1st) as the must be, if the visibility, in 
the first premise and that in the second be objectively hetera; and two 'ob- 
jectively heterical existences, one in each premise, must always be found in 
the premises of every syllogism.* And hence the general proposition that all 
colors are visible, is established beyond a doubt by the syllogistic process. 



107 
The proposition that ail sounds are audible, or that sound is, has been, and 
ever will be audible, is established in the same manner. And thus we may 
deal with all the homonical propositions in which both the subject and pre- 
dicate are the simple existauces, which we have called facial gregaria. That 
all red is red, that all sweet is sweet, or that all white is, has been, and ever 
will be white to human beings, nobody doubts, because a contrary supposi- 
tion is not only inconceivable but impossible, unless siinilia and differentia 
are homon. 

Let us-now turn our attention to capacial gregaria, and we will first 
notice figure or form. It is a proposition not worth discussing after what 
has alreadv been said respecting homonical propositions and space, that 
every aggregate existence must have some figure or form. But were ten 
millions of forms inter se differentia known to our minds (and about thingi 
unknown we cannot reason) and we should give a name to distinguish any 
one figi.re or form, each other figure, which was a simile of the figure named 
must receive the name given to the homonical figure, which name now be- 
comes a common name for all similia. If for instance we distinguish from 
other things any round ring by the name circle, then any round ring thus 
distinguished from other things, has been, is and always will be a circle 
First round ring and a circle are homon, second round ring and first arc . 
similia. Therefore second round ring and a (one) circle are homon. And so 
also with squares, cubes, triangles/parallelograms, &c. 

And it must be evident that if in any relation of parts, anything which 
may be called a quality, be found in any figure, this quality must have a 
simile in any other figure, which is a simile of the first figure. Far, all the 
relations of the space inclosed by the outlines of any figure, must be inclosed in 
like manner by the outlines of all figures which are inter se similia. Certain 
points and their relations inter se in space constitute a figure, and when we lay 
down all the points and tneir relations, which that figure can contain. One cir- 
cle and another are similia, the commensural relation of the diameter and one 
third of the circumference is in the fiist circle, i. e., the where of such com- 
mensural relation of points in space and the where of the points contained 
in the first circle are homon, therefore this commensural relation is in the 
second circle: and as circles are similia ol space, tbij relational simile is in 
all circles at any time in any where. And such is the case with all the geo- 
metrical figures. 

But if we consider the forms of animals, vegetables or minerals, we 
will find but few perfectly similia. The human form has no homonical 
standard by which to determine similia. If we should give certain and 
definite relations of points in space as the human form, we then might reason 
upon such human form with logical mathematical certainty, but our reason- 
ing would only be approximately true when applied actually to individuals. 



10b 
For the homonical standard which we have assumed, has not a simile in 
each individual of mankind; yet there is an approximation to similia in the 
forms of human beings sufficient 'usually to distinguish the human form from 
that of other animals. And this sufficient approximation to an homonical 
standard in one speces, and the approximation to an liomonical standard in 
another, enable us to affirm differentia anywhere, now, in time past, and in 
the future. We may say w 7 ith all confidence that the form of any man and 
the form of any lizzard are, have been and always will be differentia. The 
human form, though not a simiie o( any liomonical standard, is sufficiently 
distinguished by its relations from others; and were it not so, we could not, 
tell the human form from others. We can not, indeed, point out an^ particu 
lar in the form of John, and say that wherever man is found, you will find a 
simile of this particular, but we can point out a number of particulars in 
John and say with confidence that wherever man is man there will be an ap- 
proximation to these particulars. Of the* forms of animals, vegetables and 
minerals then,, we can not usually find an hpmonical type, and hence we can 
draw 7 but approximate conclusions respecting the individuals which we have 
not seen. 

Let us next consider impenetrability. We say and believe that all mat- 
ter is impenetrable; and impenitrabihty being a simple existence and the 
predicate of an homonical proposition whose subject is an aggregate exis- 
tence, we mean of course, that one of the tjregaria sine qua non of matter 
and impenetrability are homon. xlnd why do we believe this? Simply bo 
cause we believe that homon is homon in any where at any time. Take the 
proposition All matter occupies space ; and if this needs proof, we may take 
any piece of matter and we w T ill see that this piece occupies space; we will 
see also that a where occupied and a where unoccupied are differentia; then 
the'where of this piece of matter and an occupied where are homon; an un- 
occupied where and an occupied : where are differentia; but if another piece 
of matter can exist in an unoccupied where, then the where of the first piece 
and the where of the second one are differentia. But all unoccupied wheres 
in space are similia, because space is space, homon is homon; the capacity to 
occupy, therefore in any where, is the only thing that can make an occupied 
where and an unoccupied where, differentia. But this capacial gregarium 
must reside in the thing occupying, and therefore matter having this grega- 
rium and matter without it are differentia. But matter is matter, homon is 
homon, and this capacial gregarium is the sine qua non, which makes differ- 
ent pieces of matter similia, and therefore all matter must occupy space. 
Impenitrability in objects is nothing more than the capacity to remain in 
space; for, so long as an homonical obejct remains in space, the homonical 
where, in which it is, cannot be occupied by an heterical object, unless hetera 
and homon are homon, which is impossible. So long therefore, as matter is 



109 

matter, impenitrability will be its capacial gregarium. That, which has no 
where, cannot be matter, and hence matter, whose impenitrability has been 
destroyed, is no longer matter, it is no longer anything. The homonical 
where of an homonical existence called matter and an (one) occupied where 
are homon, an occupied where and an unoccupied where are differentia; but 
if the homonical matter in the homonical where be destroyed by heterical 
matter, the homonical where cannot be occupied by the homonical matter 
unless hetera and homon are homon, which is impossible ; therefore any mat- 
ter must occupy space. This, however, does not prove that matter cannot be 
annihilated; it only proves that wherever and whenever, matter is matter, it 
will occupy space ; that all matter is impenitrable. Whether matter can be 
annihilated or not, we have no data from which we can decide the question. 
Water may be inclosed in a golden ball and pressed through the gold, but 
this only proves that by such means matter cannot be annihilated. 

The use of the syllogistic process in establishing a sine qua non, by the 
singular homonical syllogism, which we have just been discussing, seems 
to be what J. Stuart Mill considers the true type of induction, when he de- 
fines induction to be "the operation of discovering and proving general pro- 
positions." Mr. Mill, however, like all other writers upon induction, seems 
to have had no definite conception of the thing for which he was on the look- 
out, and he would not have been able to have identified it, if he had found it. 
In one place induction is "the operation of discovering and proving general 
propositions;" in an other it is "generalization from experience;" in an other 
it is "that operation of the mind by which we infer that what we know to be 
true in a particular case or cases, will be true in all cases which resemble the 
former in certain assignable respects;" and again, "to ascertain what are the 
laws of causation which exist in nature; to determine the effects of every 
cause, and the causes of all effects, is the main business of induction; and to 
point out how this is done is the chief object of inductive logic." Mr. Mill 
is an able writer, but his logical induction is, in a great measure, an 
ignus fatuus. 

CHAPTER XXII. 

THE PLURAL HOMONICAL SYLLOGISM. 

Having shown in the last chapter how we generalize from experience, 
and also how in certain cases we may select a simple homonical existence 
and prove it to be a sine qua non b} r the singular homonical syllogism, we 
must pursue the syllogistic process still further and show how we reason by 
the Plural Homonical Syllogism. If we put two balls before us, we will 
say that they are hetera, i. e., that the one is not the other; if, however, we 
turn our eyes away from them for a few moments, or cover them with our 
hand, and then we remove it from them and look at them again, we will say, 



.11.0 
that they are the same balls. But by this expression we do not mean that 
the one and the other are honion, for we know that inter se they are hetera, 
but what we really mean, is, that the two balls under our eyes then are the 
identical balls under our eyes now, i. e., the two balls then and the two balls 
NOW" are homonical hetera. And before proceeding further, we must again 
explain some terms, which we will have occasion to use in our future 
inquiries. 

We have already seen that time aud space per se have no capacity to 
heterate, differentiate or incommensurate objects in time and space, that sub- 
jectively two, but objectively one homonical ball to day, so far as time and 
space per se are concerned, will be objectively homon, to-morrow and for- 
ever; we will therefore call such homa, homonical noma. But if we take 
subjectively two other balls, which are objectively hemon, they are related to 
themselves in like manner as the first two, we will call them heterical homa: 
Homonical homa and heterical homa will then be hetera. 

Again, If two homonical hetera be inter se hetera to-day, so far as 
time and space are concerned, they will remain hetera, and therefore we will 
call them homonical hetera ; but if we take two other hetera, they also will 
remain hetera, and to distinguish them from the first two, we will call them 
heterical hetera: Homonical hetera and heterical hetera will then be hetera; 

Again, If two homonical hetera be inter se similia to-day, so far as 
time and space are concerned, they will remain similia inter se, and therefore 
we will call them homonical similia ; but if we take two heterical hetera 
inter se similia, they also will remain inter se similia, and to distinguish them 
fwom the first two, we will call them heterical similia: Homonical similia 
and heterical similia will then be hetera. 

Again, If we take two homonical hetera inter se differentia, they will 
remain differentia, and we will call them homonical differentia; but if we 
take two other hetera inter se differentia, they als® will remain differentia, 
and to distinguish them from the first two, we will call them heterical differ 
entia: Homonical differentia and heterical differentia will then be hetera. 

Again, If we take two homonical hetera inter se commensura, they 
will remain inter se commensura, and we will call them homonical commen- 
sura; but if we take two other hetera inter se commensura, a like cr<se will 
be with them, and to distinguish them from the first two, we will cali them 
heterical commensura: Homonical commensura and heterical commensura 
will then be hetera. 

Again, If we take two homonical hetera inter se incommensura, they 
will remain incommensura, and we will call them homonical incommensura; 
but if we take two other hetera inter se incommensura, a like case will be 
with them, and to distinguish them from the first two, we will call them 



Ill 

heterical incommensura; Homonical incommensura and heterical incom- 
mensura will then be hetera. 

Again, If we take two hetera inter se similia, they will remain inter 
se similia, and we will call them homonical similia; but if now we take two 
heterical similia, and the homonical similia and heterical similia be inter se 
similia, to distinguish the heterical similia, we will call them similical 
similia: Homonical similia and similical similia will then be similia. 

Again, If we take two homonical similia and two heterical similia, 
and the homonical similia and heterical similia be inter se differentia, we 
will call the latter differential similia: Homonical similia and differential 
similia will then be differentia. 

Again, If we take two homonical differentia and two heterical differ- 
entia, and the one of the homonical differentia and one of the heterical differ- 
entia be inter se similia, and the other of the homonical differentia and the 
other of the heterical differentia be inter se similia, we will call such heter- 
ical differentia, similical differentia: Homonical differentia and similical 
differentia will then be similia. 

Again, If we take two homonical differentia and two heterical differ- 
entia, and the homonical differentia and heterical differentia be inter se dif- 
ferentia, we will call such heterical differentia, differential differentia: Ho- 
monica] differentia and differential differentia will then be differentia. 

Again, If we take two homonical commensura and two heterical com- 
mensura, and they be inter se commensura, we will call the latter commen- 
sura, commensural commensura: Homonical commensura and commensural 
commensura will then be commensura. 

Again, If we take two homonical commensura and two heterical 
commensura, and they be inter se incommensura, we will call the latter, in- 
com mensural commensura: Homonical commensura and incommensural 
commensura will then be incommensura. 

Again, If we take two homonical incommensura and two heterical 
incommensura, and the one of the homonical incommensura and one of the 
heterical incommensura be inter se commensura, and the other of the ho- 
monical incommensura and the other of the heterical incommensura be inter 
se commensura, we will call the heterical incommensura, commensural incom- 
mensura: Homonical incommensura and commensural incommensura will 
then be commensura. 

Again, If we take two homonical incommensura and two heterical 
incommensura, and they be inter se incommensura, w T e will call the latter, 
incommensural incommensura: Homonical incommensura and incommen- 
sural incommensura will then be incommensura. 



112 



1. 



The following list will show the terms and their relations: 

Homonical similia a.a. 



Homonical homa a.a. 
Homonical homa a 



.a.) 
.a. f 



homa. 



9. 



Differential similia b.b. C 



{■ differentia. 



Homonical homa a.a. ) y,^ ar , Q 
Heterical homa a. 'a.' [ neiera - 



1fl Homonical differentia a.b. ) . . r 
iU Similical differentia a. 'b. 1 f similia 



4. 



5. 



7. 



8. 



Homonical hetera a.a.' } i ia t« ro 
Heterical hetera b.b. ' (" lietei a * 

Homonical similia a.a. ) 



11 



Homonical differ, a.b. 
Differential differ 



t.b. [ 
c.d. f 



differentia. 



Heterical similia a. ' a. ' f 



hetera 



10 Homonical com. 2.2. ) 

12 Com'suralconi.2'2' \ commeD 



sura 



mcommensura. 



Homonical differentia a.b. ) u af ~ r „ -to Ho'ical com. 2.2. ) 
Heterical differentia c.d. J neiera - i0 Incom. com. 3.3. J 

Homonical comensura 2.2. ) , _ f -„ 1A Horn, incom. 2.3. ) _ „, 
Heterical commensura3.3. | ^tera.14 Com . incom . 2 . 3 . [commensura. 



Homonical incomens'a 2.3. 
Heterical incom'ensura 3 
Homonical sim ilia a.a. 
Similical simi 



; y hetera 15 

milia a.a. ) '-^-iV 
iliaa.'a.'h imilla - 



Horn, incom. 2.3. 
Incom. incom. 5.6. 



h 



mcommensura 



Now the following paradigms will show the syllogisms, which may 
be constructed with the foregoing terms, which syllogisms, as they have one 
homonical premise at least in each mode, we call plural homonical 
syllogisms. 

Mode First. — The homonical homa a.a. to-day, and the homonical 
homa a.a. a thousand years hence, are homonical homa; The homonical a' a' 
to-day, and the homonical homa a. 'a.' a thousand years henGe are homonical 
homa; Therefore the homonical homa a.a. a thousand years hence and the 
heterical homa a. 'a.' a thousand years hence, are similical homa. 

Mode Second — The homonical homa a.a. to-day, and the homonical 
homa a.a. a thousand years hence, are homa; The heterical homa a. 'a.' to- 
day, and the homonical homa a.a. to-day, are heterical homa; Therefore, the 
homonical h»ma a.a. a thousand years hence, and the heterical homa a.' a.' a 
thousand years hence, are heterical homa. 

Mode Third. — The homonical hetera a. 'a to-day, and the homonical 
hetera a. 'a. a thousand years hence, are homonical hetera; The homonical 
hetera a. 'a. to-day, and the heterical hetera h.b. to-day, are heterical hetera; 
Therefore, the homonical hetera a. 'a. a thousand years hence, and the heteri- 
cal hetera b.b, a thousand years hence, are heterical hetera. 

Mode Fourth. — The homonical similia a.a. to-day, and the homonical 
similia a.a. a thousand years hence, are homonical similia; The homonical 
similia aa. to-day, and the heterical similia a. 'a.' to-day, are heterical 
similia; Therefore the homonical similia a.a. a thousand years hence, and the 
heterical similia a.' a.' a thousand years hence are heterical similia. 

Mode Fifth. — The homonical differentia a.b. to-day, and the homonical 
differentia a.b. a thousand years hence are homonical differentia; The ho- 
monical differentia a.b. to day, and the heterical differendia c.d. to-day are 
heterical differentia; Therefore the homonical differentia a.b. a thousand 
years hence, and the heterical differentia .c.d. a thousand years hence, are 
heterical differentia. 



113 

Mods Sixth. — The homonical commensura 2.2. to-day, and the homon- 
ical coinmensura 2.2. a thousand years hence, are homonical commensura; 
The homonical c©mmerisura 2.2. to-day, and the heterical commensura 3.3. 
to-day are heterical commensura; Therefore the homonical commensura 2.2. 
a thousand years hence, and the heterical commensura 3.3. a thousand years 
hence, are heterical commensura. 

Mode Seventh. — The homonical incommensura 2.3. to-day, and the 
homonical iacommensura 2.3. a thousand years hence are homonical incom- 
mensura; The homonical incommensura 2.3. to r day, and the heterical incom- 
mensura 4.5. to-day are heterical incommensura; "Therefore the homonical 
incommensura 2.3. a thousand years nence, and the heterical incommensura 
4.5. a thousand years hence, are heterical incommensura. 

Mode Eighth. — The homonical similia a. a. to-day, and the homonical 
similia a.a. a thousand years hence, are homonical similia; The similical 
similia a. 'a.' to day and the homonical similia a. a. to-day are similical 
similia; Therefore the homonical similia a.a. a thousand years hence, and 
the similical similia a. 'a,' a thousand years hence are similical similia. 

Mode Ninth. — The homonical similia a. a. to-day, and the homonical 
similia a. a. a thousand years hence are homonical similia; The homonical 
similia a. a. to-day, and the differential similia b.b. to-day, are differential 
similia; Therefore the homonical similia a. a. a thousand years hence and the 
differential similia b.b. a thousand years hence are differential similia. 

Mode Tenth. — The homonical differentia a.b. to-day and the homonical 
differentia a.b. a thousand years hence are homonical differentia; The homon- 
cal differentia a.b. to-day, and tlie similical differentia a.'b.' to-day are 
similicai differentia; Therefore the homonical differentia a.b. a thousand 
years hence, and the similical differentia a.'b.' a thousand years hence, are 
similical differentia. 

Mode Eleventh- — The homonical differentia a.b. to-day, and the ho- 
mpnical differentia a.b. a thousand years hence are homonical differentia; The' 
differential differentia c.d. to-day, and the homonical differentia a.b. to-day 
are differential differentia; Therefore the differential differentia c.d. a thous- 
and years hence, and the homonical differentia a.b. a thousand years hence 
are differential differentia. 

Mode Twelfth. — The homonical commensura 2.2. to-day, and the ho- 
monical commensura 2.2. a thousand years hence, are homonical commen- 
sura; The eommensural commensura 2. '2.' to-day, a»d the homonical com 
mensura 2.2. to-day, are commensura] commensura; Therefore the commen- 
sural commensura 2. '2/ a thousand years hence, and the homonical com- 
mensura 2.2. a thousand years hence, are eommensural commensura. 

Mode Thirteenth. — The homonical commensura 2.2. to-day, and the 
homonical commensura 2.2. a thousand years hence are homonical com- 
mensura; The incommensura! commensura 3.3. to-clay,,and the homonical 
commensura 2.2. to-day, are incommensural commensura; Therefore the in 
eommensural commensura 3.3. a thousand years hence, and the homonical 
commensura 2.2. a thousand years hence, are incommensural commensura. 

Mode Fourteenth. — The homonical incommensura 2.3. to-day, and the 
homonical iacommensur 2.3. a thousand years hence, are homonical incom- 
mensura; The eommensural incommensura 2. '3.' to-day, and the homonicai 
incommensura 2.3. to-day, are eommensural incommensura; Therefore the 
eommensural incommensura 2/3.' a thousand vea;s hence, and the homoni- 



114 

cal incommensura 2.3. a thousand years hence, are commensural incom- 
mensura. 

Mode Fifteenth. — The homonical incommensura 2.3. to-day, and the 
homonical incommensura 2.3. a thousand years hence, are homonical incom- 
mensura; The incommensural incommensura 5.8. to-day, and the homonical 
incommensura 2.3. to-day;, are incommensural incommensura; Therefore the 
incommensural incommensura 5.6. a thousand years hence, and the homonical 
incommensura 2.3. a thousand years hence, are incommensural incommensura. 

If the reader has carefully studied what we have called the singular 
homonical syllogism in the preceeding chapter, the plural homonical syllo- 
gism will not need to be specifically explained. And any person can see thac 
we are not necessarily limited to two homa or hetera; we may take the ho- 
monical homa or hetera a, b, c, d, e, &c, and deal with them in like manner 
as we have dealt with two homa. 

Now if we take any simple existence in nature, any one will allow that 
this simple existence and^itself are homon ; and any one will agree also that so 
long as this simple existence and itself are homon, it and itself can not be 
hetera, and consequently it can not be a simile of itself, nor can it and itself 
be differentia. And in a previous chapter we have shown that, when we look 
upon nature, we gain our knowledge of cause, in the first instance through 
effects, which are manifested by changes. And from what we have said 
already, it must appear, that a homon per se can not change: whatever it may 
be, so long as it exists, it is the homonical homon. If then we take any sine 
qua non, impenitrability for instance, this sine qua non is impenitr^bility to- 
day, always has been and always will be, homon is homon. 

Now if we place before us an ivory ball, we have no doubts in affirm- 
ing that one of the capacial gregaria sine qua non of this ball and impenetra- 
bility are homon; and it we pat before us another ivory ball, we will make a 
ike affirmation respecting it, and therefore the first and second balls are 
similia. And if the first gregarium be located in the homonical where B, 
and the second one enter the homonical where B, the first one must take an 
heterical where. For, in the respect of impenetrability the two balls are 
similia; and therefore the homonical similia a. 'a. to-day, the one (a) in the 
homonical where B, and the other (a') in the where C, and the homonical sim- 
ilia a. 'a. to-morrow in any where are homonical similia. But respecting the 
homonical similia a.'a, to-morrow, if the second (a') be in the where B, i. e., 
if the where B occupied to-d*% by the first (a) to-morrow be occupied by the 
second (a.'), the second (a.') must have a simile in the first (a), and the where 
of this simile, and the where B must be hetera. But if (a.') the first sine qua 
non be displaced necessarily from the where B by the entrance of the second 
(a.) sine qua non, is not what has happened in a single instance sufficient to 
establish beyond a doubt that, whenever any where is occupied by an A and 
another a' enters this where, the first a must be displaced? So long as homa 
are homa, this must be the case in any part of space at any point of time. 



115 
And if this be the case with the homonical similia a, 'a., must it not always 
be the case with all similical similia? And if we call this displacement of 
one impeoitrable object by an other, a law, it must be evident that this law 
is uniform, i. e., this law and an uniformity are homon. And in a like man- 
ner we might treat of elasticity, of fluidity, of rigidity, lubricity and so on* 
And so lona: as noma are noma and similia are similia, we can not doubt of 
the uniformities in all instances. 

But again if we take two differentia, oxygen and hydrogen for instance, 
we may reason upon them in like manner and with perfect exactness. For, 
oxygen being an elementary thing, so long as oxygen is oxygen, as homon is 
homon, any particular oxygen will contain all the gregaria of any oxygen, i. 
e., each gregarium of a particular oxygen will have a simile in any and every 
other oxygen: and so also with hydrogen. And hence if any homonical pro- 
cess unite them into water in any instance, a simile of this process will unite 
them into water in every instance. So lougas noma arehoma, similia similia 
and differentia differentia, we can not doubt that a result brought out of the 
homonical differentia a.b. by the homonical process d, will have a simile of 
that result brought out of the similical differentia a. 'b. by d', a simile of the 
homonical process d. x\nd hence we must conclude that The laws of nature 
are uniform; is a proposition which is established in our minds by the syllo- 
gistic process. The result of the homonical differentia a.b. by the homoni- 
cal process d and A are homon: The homonical differentia a.b. with the ho- 
monical process d and the similical differentia a 'b.' with the similical pro- 
cess d' are similia; Therefore the result ^of the similical differentia a.'b.' 
by the similical process d' and a are similia. 

We have now said all that we deem necessary to be said at present 
while treating of the syllogism. We have given the syllogistic process a 
much more thorough analysis than it has received heretofore by writers upon 
logic, and we hope that our labors thus far will enable philosophers who 
shall come after us to see clearly the manner, application and use of the 
syllogism. We, however, must proceed further, and treat of induction, a 
subject, which, we are eoufideut, has not been understood by writers upon 
that subject. Induction, therefore, will occupy our attention iu Book II. 



BOOK II. 

CHAPTER I. 

MISNAMED INDUCTIONS. 

The processes of the mind concerned in induction, in our apprehend- 
sion,have not been understood by any writer upon logic, with whose works 
we are acquainted. Bacon is said to have been the author of the inductive 
philosophy; but his Novum Organum shows the necessity -of such a philoso- 
phy scientifically constructed rather than the actual construction in a 
methodical manner. His remarks^ as far as they go, are not systematically 
arranged, and therefore they are often obscuie; and from this reason with 
others, his suggestions, though frequently of the greatest importance, have, 
not led his successors to glean from his aphorisms the true principles of in- 
duction and to work them into a scientific and methodical system of inductive 
logic. That Bacon had in view a better aud greater system of philosophy 
jlhan subsequent writers have made out of it seems to me to be certain. The 
aids for the understanding, about which he speaks so frequently, are suggested 
here and there in the second book of the Organum, but without any scientific 
theory to cement and make his remarks understood. History and experi- 
ments, without the knowledge of the inductive processes and their applica- 
tion can not aid the understanding in gaining certain knowledge of nature's 
laws; and these processes, as far as treated of, are not brought out in a 
scientific manner in the Organum. Men have always had nature before them 
but the method of interrogating her has not been understood And though 
Bacon made a grand beginning at explaining this method, yet most subse- 
quent writers have not only, not improved upon Bacon's work, but have 
underated the val'ie of such method. 

There is no subject about which more erroneous notions prevail among 
philosophers, th&ii about the subject of the inductive processes themselves; 
and these notions, in our opinion, are grounded upon erroneous notions 
about the syllogism. Philosophers are not at all agreed, about what pro- 
cesses, when pointed out shall bt called inductive; and hence results, which 
are entirely owing to the syllogism, are often claimed as inductions, induction 
having some vague and unexplained meaning. The better way, however, to 
show what results are owing to the syllogistic process, is to explain the 
syllogism, and then the reader himself can make the application to any case, 
which may arise; this we have endeavored to do heretofore. And the better 
way to show what results are owing to the inductive processes, will be to 
explain these processes. But before doing this, from the manner in which 
the subject has been treated by authors heretofore, it is necessary, in order to 
be well understood by the reader, for us to show some things, which have 



2 
been called induction, but which it* our system do not at all come under the 
meaning, which we attach to that term. 

Archbishop Whately has- treated of induction, but his erroneous no- 
tions, as we conceive, of the syllogism, led him to misconceive the nature of 
the inductive processes; though many of his remarks are valuable in helping 
to clear the way for a better understanding of the matter. The scholar, 
however, who has done more, perhaps, than any other, in clearing the way, 
is I. Stuart Mill. His treatise upon logic is learned and able, though we 
can not, agree with him either upon ratiocination or induction. Archbishop 
Whately has well remarked that the syllogistic process is not the sole process 
necessary in reasoning in a syllogistic mannef; and we "may state that we do 
not consider the syllogistic and inductive processes together to be the only 
processes used in gaining truth, as an}' one will understand, who has studied 
the remarks made in the chapters previous to those treating of propositions 
and the syllogism in book 1. But to attempt to notice all the processes, 
which have been brought forward as inductive, but which we do not regard 
as such, would require too much room in this book, and besides, as we think, 
it will be unnecessary. • 

And first, when a name stands for, or points out a sine qua non, which 
distinguishes the existence for which it stands from others, we do nat con- 
sider that the inductive process has anything to do with proving this sine 
qua non, or with proving the general proposition, which may be constructed 
upon this sine qua non. All those truths, which we have called nominal 
truths, are each of them, a sine qua non of themselves; and hence there is no 
induction in establishing the truth of the proposition that, every color, in 
any place at any time, is a color, but the tiuth of such proposition is estab- 
lished by the singular hemonical syllogism, as we have shown heretofore. 
Neither do we consider induction to be the collecting of a sufficient number 
of instances to warrant us in believing that the instances, which we have 
seen, are fair specimens of the class. We should think strangely of a man, 
who, after having been informed that the name island distinguishes a portion 
of land entirely surrounded by .vater should start on a tour to examine this 
and that island, until he had a sufficient number of instances collected to 
warrent the inference that, all islands are surrounded by water; yet Arch- 
bishop Whately's concepiion of induction does not rise higher than this. 
The Archbishop agrees with Aldrick, that, from the examination of this and 
that magnet, we conclude that all magnets attract iron; when in truth, mag- 
netism, the quality of attracting iron, is the sine qua non of magnets, and it 
must of necessity exist in every thing, which may be called a magnet. And 
we discent altogether from Mr. Mills definition that, "induction may be con- 
sidered the operation of discovering and proving general propositions." And 
instead of believing with Mr. Mill, that induction is at the foundation of all 



3 
general propositions, we do not think that any general proposition can be 
established by induction. We therefore state to the reader that the process, 
about which we shall speak hereafter under the name of inductive, has 
nothing to do with establishing general propositions, and that such notion 
has a tendency to obscure the whole subject. 

We must also be careful to avoid another error of Mr. Mill, in con- 
sidering induction to be generalization from experience. We have heretofore 
shown that, generalization from experience proceeds upon the singular 
syllogistic process; and if we go any farther than experience and infer that 
cases to which mankind's experience does not extend, will besimilia of those 
falling within that experience, the experience is not an inductive, but a pro- 
bable one. The case given by Mr. Mill himself of the mistake made by 
mankind in infering that all swans are white because they had seen a great 
number of white swans, and not a single instance of a swan of any other 
color, shows that Ihe induction, if it Le called so, was faulty, and in our 
estimation it was no induction at all, but merely a probable inference from 
number?, the inductio per enumerationem simplicem of Bacon. Propable 
inferences may be drawn, with which we are perfectly satisfied, though we 
can not know that they are certainly true. Day and night have succeeded 
each other with perfect regularity so far as ihe experience of mankind ex- 
tends, and for that reason alone there is a strong probability if we can see no 
cause for a change that such will be the case hereafter. But from the cireu in- 
stances that no exception to a certain uniformity has fallen within the ex- 
perience of mankind, we do not infer by the inductive process that there 
will be no exception hereafter. From the continuous uniformity, extending 
thmugh experience, we are led to believe upon the ground of probability 
that the causes producing such uniformity will continue to act without 
interruption, though we know not what these causes are, nor that thev will 
cert.tinly continue uninterrupted 

The case of the naturalist inferring that all horned animals are cloven 
footed, because all those horned animals, which have fallen within the ex 
perience of mankind, are so, rests entirely upon probabilities, aud not upon 
induction unless the inductio perenumerationem simplicem be true induction. 
If it had always happened within our experience that every Friday brought 
some ill-luck, the inference that every Friday in the future will be unluckv, 
would be just as probable to our minds as the case of animals with horns 
having cloven feet, yet there is nothing in ihe nature of such inference that 
corresponds to what we mean by induction. 

Again, we do not agree with Mr. Mill in the office of induction in 
ascertaining the distance from the earth to the moon. Mr. Mill saj^s, "the 
share whidh direct observation had in the work consisted in ascertaining at 
one and the same instant, the zenith distances of the moon, a* seen from tw» 



4 
} oints very remote from one another on the earth's surface. The ascertain- 
ment of these angular distances ascertained their supplements; and since the 
angle at the earth's centre subtended by the distance between the two places 
of observation was deducable by sperical trigonometry from the latitude and 
longitude of those places, the angle at the moon subtended by the same line 
became the fourth angle of a quadrilateral of which the other three angles 
were known. The four angles being thus ascertained, and two sides of the 
quadrelateral being radii ot the earth; the two remaining sides and the 
diagonal, or in other words, the moon's distance from the two places of ob- 
servation and from the center of the earth, could be ascertained, at least in 
terms of the earth's radius, from elementary theories uf geometry. At each 
step in this demonstration we take in a new induction represented in the 
aggregate of its results, by a general proposition." Now we do not consider 
that tharehas been any induction at all in the above problem, but that, after 
the observations are made, the whole process is syllogestic; and any one, who 
has mastered what we have said heretofore in Book 1st, we apprehend, can 
make the application and demonstrate the problem by the syllogism. 

Neither do we agree with Mr. Mill that the uniformity in the course 
of nature, or what is the same thing more definitely expressed that lite 
causes with like conditions will produce like eflects in any place at any time 
is the highest induction, nor do we consider it to be any induction at all. 
Neither do we consider "this assumption," to be as an assumption involved 
in any case of induction ; nor can we consult the actual course of nature in 
this regard any farther than our experience extends, which is not sufficient 
to warrant an inductive influence. But we have shown heretofore that the 
uniformity of nature, or that like causes with like conditions will produce 
like effects in any place at any time, is demonstrated to our minds by the 
plural homonical syllogism. 

There in an other improper use of the term, induction well pointed 
out by Mr. Mill, it is the case of the navigator approaching land and being 
at first unable to determine whether it be a continent or an island ; but after 
having coasted around and having arrived at the same point from which he 
started he pronounces it to be an island. This navigator by connecting, to- 
gether all his observations finds that this land is surrounded by water, and 
every island is a portion of land surrounded by water, and therefore this 
land and islands are similia — this land is an island. Mr Mill continues to 
show that Kepler ascertained the figure of the orbit travelled by the planet 
Mars, by observations separately made but connected together in a like 
manner with the navigator, and justly concludes that there was no induction 
in the process But Mr. Mill considers that Kepler did make one inductive 
inference, when he inferred that the planet would continue to revolve in an 
elipse. Now if this inference was made upon the grounds that like causes 



5 

will produce like effects then the iaference was syllogistic; but if it was 
made upon the grounds that the planet had always gone in an ellipse hereto- 
fore, the inference was a probable one; and in no case could such inference 
be made by induction. 

These remarks might be continued at great length ; but if the student 
has mastered the syllogism, he will be able to see that many results purely 
syllogistic have been attributed by authors to induction, and that the term 
induction is very often used without any definite meaning at all. Having, 
therefore, set the mind of the reader free, as we hope, so that he will not look 
in wrong directions, we will proceed and come nearer to the subject, and ex- 
plain what we consider to be true induction. 

CHAPTER II. 

INDUCTION DISTINGUISHED. 

Having spoken in the previous chapter of certain notions of induction 
which we wish the reader to keep out of his mind, while following us in 
our future inquirers, it seems necessary now to state what we mean by induc- 
tion's well as words can express our meaning in brief, and U> give the 
reader some clue to the directions in which we propose to go in search of 
truth Induction, then, is the result of* those processes of the mind by which 
the unknown causes of any given effect are discovered; and the processes of 
the mind engaged in such discoveries are the inductive processes. We stated 
in -a former chapter that we gain our knowledge of cause, in the first ins- 
tance, through effect, i. e., we can not look upon any aggregate existence, 
and before we have the knowledge of effects, determine such existence to be 
or to contain a potential cause of any given effect. And in studying the in 
ductive processes we must always have some given effect before our mind 
and from it determine the causes: the inductive processes have nothing to 
do in taking causes and from them determining effects. If indeed we take 
two elementary substances and put them together and a certain effect follow 
we take this effect and determine that those elementary substances were the 
causes of it; and when we have done so, we have also, from the correlative 
natures of cause and effect, determined that the phenomenon which we call 
an effect, is the effect of those causes; but we must always keep the effect in 
view, it must be in view always before the inductive processes can have any 
thing upon which to operate, while the causes of a given effect may be and 
always are entirely out of sight or without our knowledge when the induc- 
tive processes commence to search for them. If the reader wil! bear this in 
mind it will free the subject from much obscurity, which otherwise sur- 
rounds it. 

And since cause and effect are always involved by the inductive pro- 
cesses, it is necessary also, to put the reader upon his guard that he may not 



6 
confound what are called a priori and a posteriori reasonings with induc- 
tion. After that we have gained the knowledge of certain effects and their 
causes, we look upon these causes and their conditions, and infer, by the 
plural homonical syllogism, what effects will follow, without waiting to 
witness such effects by our senses. For instance, if a cannon be loaded with 
dry powder and a man be about to apply a match to it, by the plural homoni- 
cal syllogism we infer that there will be an explosion This application of 
the syllogism when we have the conditions as the homoyiical similia or 
differentia, whose effects we know in the premises, and from them we infer 
the effects of similical similia or differentia, whose effects have not yet 
transpired in time and space, is called a priori reasoning, or reasoning from 
cause to effect. Induction, however, has nothing to do with it. 

On the other hand, if we see a cannon and hear the report of its dis- 
charge and we be asked, what is the cause of this report, from our former 
knowledge of such effect and its causes, by the plural homonical syllogism, 
we infer the cause of this particular effect. And this application of the 
syllogism, when we have an effect whose causes and conditions we know as 
the homonical homon in the premises, and we infer the causes and condi- 
tions of a similical homon, whose causes and conditions are not witnessed by 
our senses, is called a posteriori reasoning, or reasoning from effect to cause. 
But there is no induction in it. 

Both A priori and a posteriori reasonings are entirely syllogistic. In 
both, some particular casejias brought by induction the knowledge, in. the 
first instance, of a certain effect and the causes and conditions of it to our 
minds, and then this case furnishes the premises for the plural homonical 
syllogism to work with, either a priori or a posteriori. But when the 
causes of an effect, an homonical homon, are unknown, no inference can be 
drawn a posteriori respecting the causes of a similical homon; neither can 
any inference be made a priori respecting the effect of similical similia or 
clefferentia, when the effect of homonical similia or differentia, the effect of 
such causes, is unknown to us. The knowledge of certain effects with their 
causes is already in the mind before a posteriori or a priori reasonings 
begins. The inductive-processes take hold of any given effect, the causes of 
any similical effect and also of this given effect being without our knowl- 
edge, and search out and induct the conditions and causes of the given effect. 
Keeping, then, hi mind that, a priort and a posteriori reasoning are syllo- 
gistic and thpt they proceed from certain known cases to infer respecting 
similical cases, while the inductive processes proceed from a given phenome- 
non to make knoA-n to us the causes and conditions of that phenomenon, we 
will proceed farther, hopifig that we will not be misunderstood 

Now in speaking of cause and effect, it is usual with philosophers to 
c,vli the cause a;i antecedent and the effect the consequent. These terms, 



7 
antecedent and consequent, have reference to the relations of points in time, 
and we have already shown heretofore, that time possesses no capaeial gre- 
garia and that it can not be the cause of any change or effect. And therefore 
it we say that a cause is an antecedent, we must mean only that the existence 
whatever it may be, to which we refer as cause, occupied a point in time 
prior to the point occupied by the existence which we call the effect. And 
although this be true, yet it does not with any defiuiteness determine a cause. 
If we say that a cause is anfanterpeclent of an effect, i. e., a cause and an an- 
tecedent are homen, we may still enquire what antecedent is referred to as 
connected with any given effect, for there are many things which existed in 
nature prior to John Smith's being intoxicated, t and which antecedent is 
connected with this effect? It is, therefore, merely the condition of a cause 
that it exist antecedently to an effect; but antecedent is a term which can 
not be used as synonomous with cause. 

Now we have shown heretofore that time and space can not be the 
causes of any thin*?; they are however the conditions of all causes and effects, 
and they are the only things of which we shall speak in our future inquiries 
as conditions. Every thing in nature which can be a cause, can be cause 
only upon the conditions of time and space, and that which has once been a 
cause, will in like conditions of time and space in the future be a cause again. 
A condition which presents the absence of a preventing cause is sometimes 
confounded with a cause, as the absence of the air in a pump is, sometimes 
said to be the cause of the water rising in it. This however is but a condi- 
tion of space. 

We define causes therefore, to be the capaeial gregaria of the aggregate 
existences from which given changes or effects spring. To go behind the 
eapacial gregaria of aggregate existences and inquire into the ontology of 
these capaeial gregaria is bo part of our undertaking at present. We may 
say, indeed, that they are the maifestations ©f the Deity's will, i. e,. that they 
are the capaeial gregaria of the Almighty himself made tan^able to us; but 
we take these capaeial gregaria of existences made known to us, as the only 
causes of which we shall treat and we shall legarcl them as the primary 
causes of all the effects in nature. If an}' one shall say that the Almighty is 
still a prior cause, we have no objection. 

And it will occur to almost any one, after what has been said about 
cause and effect in a previous chapter, that an homonical capaeial gregarium 
per se can not be a cause of any given effect; there must be heterical gregaria 
implicated before any effect can be produced. If we take an ivory ball, 
which possesses the capaeial gregarium of unpen itrability, i. e., the power 
to remain in space, we must see that this capaeial gregarium per se can pro- 
duce no effect whatever. If the ball be at rest its impenitrahility can not 
start it, and if it be in motion its impenitrability can not stop it; the impeni 



8 - 

liability in the ball can per se produce nothing. But if an other ball pos- 
sessing also impentrability be brought to bear upon the first one, the heterical 
impenitrabilities, on3 in each ball, can inter se produce an effect. Homon 
per se must always remain homon, and per se no effect can spring from an 
homonical gregarium ; and hence all effects in nature are produced, not by an 
homonical gregaridm, but by heterical gregaria. And as the capacial gre- 
gariaof the aggregate existences, from which changes spring, are the causes 
of all the phenomena of nature, it is necessary in seeking for these causal 
gregaria of any effect, to find, in the first place, the aggregate existences 
possessing the said gregaria, and to seperate them from others. 

And in contemplating the aggregate existences, whose capacial grega- 
ria are causes, it will readily appear that aggregate existences may be divided 
into primary, secondary, tertiary and quartuary aggregations. By a primary 
aggregate existence then, we mean what is usually called an elementary 
substance, and by secondary aggregations, those substances compounded of 
two elements, by tertiary aggregations, substances compounded of three 
elements, if such compounds exist in nature, and so on. And if we take any 
primary aggregate existance, a jar of oxygen for iustance, as this is an ele- 
mentary thing, it contains all the capacial gregaria of any oxygen. For if 
any other oxygen can be found with a less number of capacial gregaria, then 
the first jar was not elementary. But if we examine any elementary oxygen, 
as all other oxygen is a simile of that which we have examined, any experi- 
ment with certain oxygen giving a certain result will under like conditions 
give a simile of that result with any oxygen; and so also with any other 
primary aggregate existence. And the differential elements constitute the 
primary aggregate existences in which reside the capacial gregaria which 
are the primary causes of all effects in nature. These elements combine and 
form chemical compounds, which possess capacial gregaria different from 
those possessed by either of the elements entering into them. 

Now every capacial gregarium possessed by a primary aggregate ex- 
istence, is a sine qua non of that aggregation, and it has a simile of itself in 
every other aggregate existence, which is a simile of the given aggregation; 
and this is true also of all compounds. And hence we can experiment upon 
all aggregate existances, and by the homonical syllogism, infer from the 
result in any case the results in all cases of similical similia or differentia. 

And the first things to be determined by observation or experiment, 
about aggregate existences, are the conditions of time and space by which 
their capacial gregaria are regulated. And if we find by observation or 
experiments upon nature that, a certain gregarium of a certain aggregation 
is conditioned in a certain manner, we know that a simile of that gregarium 
in similar aggregations, will be conditioned in a similia manner, and in like 
manner arid with like inferences, we may experiment with the gregaria in 



9 

fasciculo, with aggregate existences themselves. Having now cleared the 
way, as we hope, we will in the next chapter proceed to explain the conditions 
of time and space, which regulate the causal gregaria, and we will then see 
the manner of proceeding to some extent, and the reader will be able to un- 
derstand better, what we mean by induction. 

CHAPTER III.. 

CONDITIONS OF TIME AND SPACE. 

We have already said that the conditions of causes and effects are time 
and space; we have also shown, that not an homonical gregarinm but heter- 
cal gregaria are the causes of every effect. And in a previous chapter upon 
cause and effect we showed that, in every effect some homon becomes hetera 
or some hetera becomes homon, some similia become differentia or some 
differentia become similia, some commensura become incomensnra or vice 
versa; this, we saw, is a condition of causation. And if we take two ivory 
balls, each of which possesses impenitrability, we must see that the impeni- 
trabilities of the balls are hetera in space; but we must see also that, unless 
these hetera in space occupy an homonical time, i. e., unless their times be 
homon, no effect can be produced by them inter se. If an effect is to be pro- 
at a certain point of time between two ivory balls, but before that point of 
time come, one of the balls be annihilated, we must see that the proposed 
effect can not transpire from the want of an homonical time for the two balls. 
Those existences, which existed yesterday but not to-day, can not be the 
causes of effects, which begin to transpire to-day, i. e., causes must possess 
an homonical time with that point in which the effect begins to transpire or 
originates. And hence let the effect be the removal of a cart from a certain 
place to another upon a hill, and let us take it for granted that some horse 
drew the cart up the hill, and suppose we wish to ascertain the individual 
horse that did it. In the first place we must ascertain the homonical time in 
which this effect occurred, then we may think of Bucephalus the horse of 
Alexander; but we know that he could not have done it, if the times of 
Bucephalus and of the effect are hetera. And we know that no other horse 
than one, whose time of existence is homonical with the time of the effect, 
could have done it. But any horse, whose time is homonical with that of the 
effect, may have done it, i. e., such horse fulfills the condition of time. And 
hence all aggregate existences possessing the causal gregaria of any given 
effect, must be synchronous with the transpiration of the effect, i. e., their 
times and the time of the beginning of the effect must be homon. 

Let us next look into the conditions of space. For, as all the acting 
causes ot any given effect must be synchronous and in space, we must deter- 
mine the conditions of space; and where the conditions of space can be de- 
termined, we know that, no aggregate existence, outside of those conditions 



10 
in any given case, can be an aggregation, which contains the causal gregaria 
or a causal gregarium of the given effect. And we must remark that, where 
two aggregate existences contain the heterical gregaria, which are the causes 
of any given effect, these gregaria must operate through the space situated 
between the two aggregations. 

A B 

If A and B be two aggregate existences with a certain space between 
them, and A put forth certain energies, these energies must take some direc- 
tion in space; and unless they take the direction towards B, the energies of 
A and B can not meet in an homonical where, and unless the heterical ener- 
gies come to an homonical where, no effect can follow. 

D— — A B -0 

Suppose, for instance, that the enegies of A take i.lie direction only 
towards D, and the energies of B only towards C, then the spaces of these 
heterical energies will always remain hetera, and no effect can follow from 
tnese heterical energies inter se. The conditions of aggregate existences in 
space, therefore, necessary to causation, are that, the heterical gregaria pos- 
sessing heterical wheres, shall find an homonical where, i.e., that (heir whores 
shall in some point of space come to bo homon. And it will readily be sug- 
gested that, though these energies may take the direction towards each oilier, 
yet they may not meet. 

A D B 

Thus: Suppose A to be a magnet and B an iron riling, if A's energies 
terminate at C and B's at D, then they have not found -an homonical where, 
and therefore no effect can follow. 

Now a homon of time and a homon of space are the conditions sine 
quibus non of causation; and all the gregaria, which can be causes, must 
come into these two homonical hetera. And hence whenever any effect 
takes place, these conditions have been fulfilled; and the object of inductive 
inquiry is to find, not onjy what objects fulfill these conditions, but also what 
objects operate, become acting causes in these conditions, i. e., what gregaria 
in these conditions are the sine quibus non of any given effect. And we 
must always recollect that, we must have a certain effect in view, and that 
effects inter se similia may be produced by sets of causes, inter se simiha, i.e., 
by similical similia or similical differentia. And as gregaria are found in 
aggregations, we must first determine the aggregations containing the causal 
gregaria of any given effect to this task we will row proceed. 

CHAPTER IV. 

HETERICAL INDUCTION. 

We have heretofore treated of simple heteration and shown that the 
power of the mind to heterate depends upon time and space. The succession 



11 

of our own thoughts in time enables us to heterate them, and the revolution 
of the earth and of the heavenly bodies in lime enables us to fix* upon any 
particular period of time and hold its relations in our mind. By the where 
of ourselves and the where of other objects in space and their relations inter 
se we are also enabled to locate a particular where in space and preserve its 
relations in our minds. And although we may not always be able to point 
out the precise point of time, in which a given effect begins to take place, we 
can generally come near -enough to that period for the purposes of heterical 
induction; and so also we can come sufficiently near to the precise where in 
space of a given effect. Simple heteration is sufficient to bring us to the 
point ot time and the point of space of any given effect i.nder consideration 
of the inductive processes. And when we have the period of time in which 
any given effect took place, as the cause of that effect must have been inter 
se synchronous and have touched upon some homonical point of that period 
of time, no aggregations before or since that period could contain the causal 

; gregaria of that effect. If the iEnead was written in the age of Augustus, 

,' no person, who lived and died before that age, or who has been born since, 
could have written it. And hence if we know the period of time in which 
any given effect took place, all aggregate existences, which have not an ho- 
gnonical time with that period, are immediately heterated from the causes of 

i the effect by our minds; and this is heterical induction. For, when .we have 
ihrovvn out those existences, which could not have been the causes, we have 
before us other existences, which may hare been the causes, and by casting 
out the former we have led in or inducted the latter. And were there but 
two aggregate existences in esse at the period of time of the effect, as there 
must have been heterical gregaria concerned in producing it, we would know 

' by the heterical induction of aggiegations by their times alone that, these 

, two existences contained the causal gregaria of the effect. 

But although the heteration of objects from the time in which any 
given effect takes place, by throwing out many aggregations which could not 

J contain causes of the effect, narrow the field in which the causes are to be 

j found. Yet there are afterwards so many aggregate existences in esse 
synchronous inter se and having times homonical with that of the effect, 

j and any of which, therefore, so far as time is concerned, may have been 
causes of the effect, that after that we have determined the homonical time of 
the effect and determine also what existences have times homonical with 
this, we are still unable to tell which of these contemporary existences con- 
tained acting causes in the present instance. We have, therefore, to proceed 

; farther and heterate the wheres of objects from the homonical where in 
which the effect took place. Although this be an easy matter in s me i: - 
stances, vet in others it is attended with great difficulties. If we seo an ob- 

! ject in motion by heterical impenetrabilities, if a ball be started by the impact 



12 
of some other object, every object, which at the homonical time of the effect's 
beginning, was outside of the homonical where of impact, i. e., whose where 
and the where of impact were hetera, can be immediately heterated by the 
mind from the causes of the effect. And so also, from the very nature of 
compounds, we know that, the ingredients compounded must come in contact 
or they would not enter into compounds together. 

And althogh we can not tell but that other existences than those in- 
gredients w T hich enter into compounds, may have something to do with the 
compounding of those ingredients, yet if the action of these other existences 
be always constant at all times and places, whenever and wherever a given 
effect is offered to our senses, for all practical purposes their action may be- 
omitted in our considerations without any error to our principles or results. 
Thus; although we may not be able to heterate the space, which bounds and 
limits the capaciai gregaria of the north polar star, from the space in which 
pine shavings are burning, yet if the influence of t!»e north star be constant 
whenever and wherever shavings and fire are found upon our earth, for all 
practical purposes we may omit this influence in our considerations and seek 
after other aggregat'uns, whose capaciai gregaria we can determine and 
limit in space; and if their space and the space in which shavings are burn 
ing be hetera, we may immediately heterate those other aggregating from the 
causes of the effect. And hence, whenever, for instance, we find soap, we 
feel assured that no ingredients outside of those which have come in contact, 
can contain the causes of soap, or at least we may look tor and receive as 
causes, if not all of the causes, some capaciai gregaria container in the in- 
gredients, which have come in contact when soap came into existence as an 
effect. 

But in numerous instances, for the purposes ot the heteiical induction 
of aggregations in space, we must follow Bacon's rule of varying the circum- 
stances, i. e., we must find what capaciai gregaria of aggregate existences are 
within the homonical time and place of given effects in one and the other in- 
stance of similical effects. Sometimes by observation upon numerous instan- 
ces of similical effects in nature, we are able to heterate aggregate existences 
from others containing the causal gregaria; and very frequently we can do this 
by experiment. If, in the consideration of compounds, for instance, a chemist 
can analyse and find a certain portion of water to contain the primary aggre- 
gations, oxygen, hydrogen and sulphur, in one instance, and in another in- 
stance, he find a portion of water to contain oxygen, hydrogen and potasium, 
he may then, by the latter instance, heterate sulphur from the sine quibus non 
of w T ater; for, in the latter instance, water occurs without sulphur being in 
the homonical space of the effect: and by the former instance he can heterate 
potasium from the sine quibus non of the effect. But it is not quite clear 
from the above analysis of the chemist, that both potasium and sulphur can 






13 

be absent from the water; for, oxygen and hydrogen may not unite, for any- 
thing we yet know, into the compound of water, without the presence of 
either tne one or the other of these substances. But if tne chemist find a 
portion of water containing only oxygen and hydrogen, he may then heterate 
all other aggregations from the sine quibus non of water. But neither oxygen 
nor hydrogen can tee heterated from the causes; for, the}- are, each of them, 
primary aggregations, and were one ot them taken away, there would not be 
left neterical gregarm to produce an effect. Now if a chemist can take cer- 
tain elements and by them produce a compound or any given result, the mode 
of making neterical inductions in the case is the same as in analysis. He 
must wait until he perceives the effect, before he can heterate any object from 
t lie causes of it. The only difference is that in analysis he must seek after 
the aggregations, which arc in the homonical time and place of the effect in 
different instances, while in synthesis he already knows the aggregations in 
the homonical time and place of the effect without iuquiring after them. 

And in general, if we suppose any given effect, to contain in its homon- 
ical time and place, the aggregations represented by a, b, c and d, in one 
instance, and in another instance a, b, e, f, and in still another a, b, g, h y 
we may, from the consideration of these three instances, heterate each of the 
aggregations severally, excepting a and b, from the sine quibus non of the 
effect; though it is not certain that a and b alone could produce the effect 
withoat the presence of some of the others, unless we can find an instance in 
which they alone are present. Bacon's rule of varying the circumstances, or 
©f examining different instances of similical effects, it wilibe perceived, ena- 
bles us to heterate, from the causes in certain cases, objects occupying the 
homonical time and space of an effect; one instance can be used to enable us 
to heterate some of the aggregations from the sine quibus non of another. 

This matter of varying the circumstances and thereby gaining the 
data from which neterical induction can proceed may be explained in a little 
different manner from that already given, though it comes to the same thing. 
Thus; if we mix together three gasses represented respectively by a, b, and c, 
and we apply this mixture to a piece of white paper, for instance, and ob- 
serve the change or effect, which takes place in the paper, anil we then applj' 
the three gasses, a, d and e, and observe also the effect upon the paper, and 
we find the two effects to be inter se similia, the latter instance enables us to 
heterate b and c from the sine quibus non of such similical effects, and the 
former instance enables us to heterate cl and e Irom the sine quibus non, 
leaving the effect to take place between the capacial gregaria of a and of the 
paper. If we represent the paper by x, we may say, a, b, c and x produce a 
given effect, which we observe upun x, but a similar effect is produced upon 
x by a, d, e and x, and therefore, b and c are not sine quibus non of such 
effects, nor are d and e. And if a, b and c, each of them, leave changes upon 



14 
the paper, which can be inter se discriminated, which changes may be rep- 
sented respectively by the capitals A, B and C, and in an other instance, a, d 
and e, produce changes, which can be discriminated inter se, we may then 
find from the gregaria of a, b, c and x the eflecls a, b, c, and from the gre- 
garia of a, d, e and x, the effects, a, d, e, and from these data we can heterate 
b and c, and d and e, from the sine quibus non of the effect a &c. 

Heterical inductions are made daily in the transactions of life and al- 
ways have been so made, though like the syllogistic process, the modus 
operandi of the mind has not been well understood. A very simple case of 
heterical induction is continually made before courts of law. If a man be 
indicted for murder and an alibi be proven, i. e., if it be clearly shown, that 
the person charged with the crime, w 7 as at the time when the crime was com- 
mitted, a hundred miles from the place in which it w*as done, the accused is 
heterated from the causes of the murdered man's death. The principle of 
heterical induction may be summed up in the following heterical proposi- 
tion ; whatever is absent from the homonical time or place of a given effect, 
and the causes of that effect, are hetera. 

CHAPTER V. 

HOMONICAL INDUCTION. 

In the previous chapter we explained the modus operandi of the mind 
in separating those aggregate existences, whose gregaria can not be causes of 
a given effect from other aggregations, whose gregaria may be the causes, so 
far as time and space are concerned, i. e., their times and wheres fulfill the 
conditions of causation. In the present chapter we must show the process of 
the mind in determining what aggregations fulfilling the conditions of time 
and space, and the aggregations containing the causal gregaria are- homoni- 
cal hetera. Although we may heterate all other objects from the homonical 
place of a given effect at the time the effect took place, excepting a, b, c, } r et 
it is not certain that a, b, c, each of them, contain the causal gregaria of the 
given effect, nor is it certain which of them do contain causal gregaria. 
Three men may have hold of a rock when it begins to more, and yet one of 
them may have done all the lifting. And supposing that lye, sand, sawdust 
and adipose tissue be put together in a kettle and boiled, and soap be the 
result, which of these ingredients contained the causal gregaria of the effect? 
We might, no doubt, heterate some of these ingredients from the causes in 
the manner pointed out in the last chapter, but our object now is not to find 
existences, which in relation to the causes of the effect are heterical, but to 
find the aggregations, which are homonical with these containing the causes. 
And in order to find the homonical aggregations we must again follow Ba- 
con's rule of varying the circumstances Suppose we take lye, sawdust and 
sand without any adipose matter and boil them just as spoken of above, and 



15 

find that no soap is produced, we may then conclude that adipose matter was 
a sine qua non of soap in the first experiment. And hence when we wish to 
ascertain whether any one of the aggregations, fulfilling the conditionsof the 
time and place of a given effect, be a sine qua non ot that effect, we first as- 
certain, if possible, all the aggregations fulfilling those conditions, and then 
we find an other case having all the aggregations as before, excepting that 
aggregation, whose gregaria as sine qaibus non, we wish to try; and if in the 
latter case the effect is not produced as in the former one, then this 
aggregation left out of the latter case was a sine qua non of the 
effect in the former c.ise. Thus; if in one case we find the aggrega- 
tions fulfilling the conditions of the time and place of the effect a, to be 

a, b, c, and d, and in an other case we find a, b and c without d in like condi- 
tions as befove, without the effect a, we then have the data from which to 
make the homonical induction, that d was a sine qua non of a. That the 
sun is a sine qua non of day may be proven by taking the case of a bright 
day and a case in the same day, when the sun is eclipsed by the interposition 
of the opaque body of the moon, or when the earth revolves and takes us 
away from the sun. 

And it is no matter which of the two cases, one of which contains all 
the aggregations and the other all excepting one, come under our observation 
first. If a, b, c and d, be found in certain conditions, and then e also come 
into those conditions and then the effect a immediately commence, all the 
data of the two cases required are furnished. Before the sun rises, we have 
the aggregations, a, b, c, . .p without day; when the sun rises we have the 
aggregations a, b, c . .p and the sun, and then it is day. And if we can find 
cases by which we can thus try successively each one of the aggregations 
fulfilling the conditions ot time and space, we may find, by homonical in- 
duction, all of the aggregations containing all the causal gregaria of any 
given effect. But we must be sure that the case, in which the effect does not 
occur, contains all the aggregations excepting the one, which we are trying 
as to its being a sine qua non, and which, the ease, in which the effect fol- 
lows contains. Thus; if the case, in which the effect a, follows, contain the 
aggregations, a, b, c, d and e in an homonical time and place, and we wish to 
see whether a, was a sine qua non of that effect, we must find a case in which 

b, c, d and e are found in a similical time and place without the effect. 

If there be more aggregations in the case in which the effect does not 
follow, i, e, if there be b, c, d, e and f in the case without the effect a, and a, 
b, c, d and e without f in the case where the effect follows, as the effect a does 
not follow in the former case, the additional aggregation f would not vitiate 
our inference respecting a's being a sine qua non in the latter case, unless 
some effect clue to f should prevent the effect a in the former case. If a, b, c, 
d and e be found to make a compound in the condition g, and b, c, d, e and f 



16 
remain but a mixture in the condition g, we may infer a to have been a sine 
qua non in the former case, unless f be a preventing cause in the latter one. 
But for entire certainty it is . necessary that the two cases agree in the aggre- 
gations except the one which we are trying. If we have a given effect a, 
with the aggregations a, b, c and d, in one case, and in an other case we have 
the aggregations b and c only and without the effect, we can not tell which or 
whether both a aadd were not sine quibus non ©f the effect a, in the former* 
case. The principle of homonical induction may be summed up in the fol- 
lowing homonical proposition ; whatever existences are sine quibus non in the 
homonical time and place of an effect and the causal gregaria of thai effeet, 
are homonical. • 

CHAPTER VI. 

DIFFERENTIAL INDUCTION. 

We have alread}' seen that the homonical a and the homonical a, 
through their times are hetera, are in space homon, i. e., they are in 
the same where at any given point of time. We have also seen that the 
homonical a and the heterical a, though their times may be homon, 
-are hetera in space, i,e, one a, has a certain where and the other a, has an 
other certain where, both of which wheres may be occupied at the same time. 
We have also seen that hetera lie at the foundation of causation, and that 
things inter se similia, and also things inter se differentia, must be inter se 
hetera; and hence either similia or differentia are the causes of every effect. 
The homonical a, and the heterical a, are inter se hatera, they are also inter 
se similia, but a, and b, are hetera and they are also inter se differentia. 

Now as the gregaria of aggregate existences are the causes «f all effects 
and as there must be heterical gregaria concerned in the production of every 
effect, and as the heterical gregaria concerned must be inter se similia or 
differentia, it is the province of differential induction to eliminate those gre- 
garia, which, with reference to the causal gregaria of an effect existing in 
either of the aggregations in the homonical time and place of such effect, are 
differentia. And in order to do this, we must first make heterical and homon- 
ical inductions of aggregations, (we may then also make heterical inductions 
of gregaria, which is as far as Bacon pushed induction) and then we must 
make differential inductions in the method about to be explained. And in 
order to understand the matter thoroughly, let us approach the subject by 
first clearing the way. Suppose we take two aggregate existences, whose 
gregaria we know, and suppose the gregaria ot the . first aggregation to be, a, 
b, c, d and e and no more, and the gregaria of the second aggregation to be a, 
b, g, h, i, and no more, and suppose that in an homonical time and place, by 
heterical andj homonical inductions of aggregations, a certain effect, which 
we will call a, to spring from these heterical aggregations; then we can not 



17 
tell, whether the effect a, sprung from the simiiia a and a, or b aud b, or from 
the differentia a and b, b and b, or c and i &c. But supposing the effect to 
have sprung from but two heterical gregaria, these heterical gregaria must be 
located, one in each aggregation, and not both in the same aggregation, Oth- 
erwise the effect w 7 ould spring up in a single aggregation and the two ag- 
gregations would not be sine quibus non in the homonical time and jjlace of 
such effect, as we may have determined to be the case by a previous homonical 
induction, and without a previous homonical induction of aggregation ', 
differential induction of causal gregaria can not proceed. 

But suppose we take five aggregations, whose gregaria we know,, the 
the gregaria of the first being a, b, c, d aud e, and no more; those of the 
second a, b, c, d, and f, and no more; those of the third a, b, c, e and f, and 
no more; those of the fourth a, b, d, e and f, and no more; those of the fifth 
a, c, d, e and f, and no more. Now we can conclude, by heterical induction, 
that the effect, which springs from the first and second aggregations, is not 
caused by the simiiia e and e, for e does not exist in the second aggregation; 
and the effect which springs from the first and third, is not caused by the 
simiiia d and d; and the effect, which springs from the first and fourth, is 
not caused by the simiiia c and c; and the effect, which springs from the first 
and fifth, is not caused by the simiiia b and b. If now the four effects be 
inter se simiiia and in view of the above state or the case, we look upon the 
second aggregation, we conclude by heterical induction that, in that aggre- 
gation e was not a sine qua non of the effect, which sprung from the combi- 
nation of the first and second aggregations; and hence a simile of it is not a 
sine qua non in any other aggregation, which may combine with a simile of 
the first aggregation and produce a similical effect. And in the other instan- 
ces, we may eliminate by heterical induction, d from the third aggregation, c 
from the fourth, and b from the fifth. 

We have not been speaking above of any other effects than these aris- 
ing from the given combinations of the given aggregations, whic.i by pre- 
vious heterical and homonical inductions we know to oe the aggregations 
containing the causal gregaria, and the gregaria of each of which aggrega- 
tions we know also. There may, for all that yet appears, however, be other 
aggregations containing causal gregaria of effects, which, with reference to 
the given effects spoken of above, are simiiia, and yet the causal gregaria 
of the other effects, with reference to the causal gregaria of the given 
effects, may be differentia. But suppose there be other aggregations 
containing other causal gregaria of an heierical effect A, these other 
causal gregaria, with reference to the causal gregaria of the homonical 
A, the effect above spoken of, must be either similical differentia, in which 
case the heterical effect is but another instance of like causes, i. e., the causal 
gregaria of the lumonical A being the homonical. differentia, a in the first 



18 
aggregation and fin the second, for instance, if the causal gregaria oi an 
heterical A', A and A' being inter se similia, be similical differentia, the causal 
gregaria of the heterical A' are the similical differentia a' and f ; or the causal 
gregaria oi the heterical A, with reference to the causal gregaria of the ho- 
monical A, must be differential differentia, i. e., the causal gregaria of the 
homonical A C being the homonical differentia a and t, for instance, the causal 
gregaria of a heterical a, may be the differential differentia e and g, tor instance 
foi aught that jet appears. But in no case, the causal gregaria of the homonical 
A being the homonical differentia a and f, can the causal gregaria of an heterical 
A be,with reference to the causal gregaria of thchomonicsl A,similical similia ; 
for the similia a and a, b and b, or d and cl, &c, to be similical similia with 
the homonical differentia a and b, is absurd and impossible. 

But supposing the causal gregaria of an homonical A, to be the differ- 
entia a and f, may not the causal gregaria of a similical A, be inter sc similia, 
such as k and k, y and y, or z and z ? Now it we contemplate the causal 
gregaria of the homonical A, and those of the similical A, as ihe two a's are 
inter se similia in every respect, and as each uf the causal gregaria of both 
a's is not an aggregation but a simple gregarium, the effect produced by a 
and f inter se can not be a simile of an effect produced by a and a, inter se, so 
long as homon is homon, and similia are similia; and if a can originate upon 
a' a simile of the effect, which f originates upon a, then a and 1 must be inter 
se similia, which is absurd. If a certain vibration of the atmosphere in con 
nect.on with the aparatus of the ear produce a certain sonm,, then a simile 
of that sound, the aparatus of the ear remaining the same, can not b<j 
produced but by a simile of the given vibration'. 

But in the case considered above, the causal gregaria in the first in- 
stance being by supposition the differentia a and f, and in the second instance 
the similia a and a, one of the causal gregaria (a) in the first instance and 
one (a) iu the second are inter se similia; that no effects inter se simiiia can 
spring from such sets of eausal gregaria, is evident. But an effect, an ho- 
monical a, having sprung from the causal gregaria, the homonical differentia 
a and f, may not a similical A, spring from the similia, g and g? In the first 
instance a originated upon f, an homonical effect A, and we see that g cannot 
originate upon f, a simile of A, unless a and g be inter se similia; but in the 
first instance, by changing the mode of expression without affecting in any 
manner, the result, f originated upon a, the homonical effect A, and g cannot 
originate upon a, a simile of A, unless g and f be inter se similia; but a is an 
homonical gregarium and g is an homonical gregarium, and inter se they are 
differentia. Now two gregaria inter se differentia can not in their action be 
inter se similia unless similia and differentia be inter se similia, which is 
impossible. And if a cannot act towards f, as g acts towards g, and if f can- 
not act towards a, as g acts towards g, the results of the actions between a 



19 
and f, and between g and g, can not be inter se simiiia. And an homonical 
effect a, having sprung from the homonical differentia a and f, we may rea- 
son in like manner respecting the effect, which must spring, if at all, from the 
differentia] differentia g and h. So too if an effect spring from the simiiia a 
and a, no similical effect can spring from the differentia a and b, c and d, &c, 
nor can a similical effect soring from differential simiiia as b and b. or c and 

x CD J 

c, &c. Of the differential elements of the alphabet, no other two can be 
conjoined so as to produce the sound resulting from* ab; and so it must be 
throughout nature. And hence it must appear that effects inter se simiiia in 
every respect must be produced by similical gregaria, either similical simi- 
iia or similical differentia; differential simiiia or differential differentia can- 
not produce similical effects. And therefore if two or more aggregations 
come into the homonical time and place of an effect, we first find by heterical 
and homonical inductions of aggregations, the aggregations from which the 
effect sprung, then we look for other instances containing a simile of one of 
the aggregations from which a similical effect sprung, i." e., we vary the cir- 
cumstances, and by doing so we are often able by 7 heterical induction of gre- 
garia to eliminate certain gregaria from the differential aggregations combined 
with the simiiia of the other aggregation in the given instance; then we pro- 
ceed farther. 

And it must be remembered that two gregarial simiiia cannot exist in 
tlte same aggregation. Thus; iron possesses hardness, and there is an ho- 
monical hardness in this piece and an heterical hardness in that piece, 
and inter se the homonical hardness and the heterical hardness are gregarial 
simiiia; but there cannot be two hardnesses in an homonical piece 
of iron; all the gregaria in a single piece or particle of iron are inter 
se differentia. Now when effects are produced between two aggergations, 
these aggregations either disappear in a measure and merge in the 
effects, as in chemical compounds, or the effects, which our senses witness 
are grounded in one of the aggregations or in both. When oxygen and hy- 
drogen unite and form water, the two aggregations, in a measure merge in 
the effect — water, i. e., although the weight, impenitrability, &c, of the sepa- 
rate elements remain as gregaria of the compound, yet some of the gregaria 
of each Element seem to have disappeared and to have merged in an effect, 
whose gregaria with reference to the gregaria of either of the elements are 
differentia; but if we apply oxygen to steel, we witness an effect grounded in 
the steel. Having now cleared the way, as we hope, we may proceed to diff- 
erential induction. 

Suppose then, that we take a certain aggregation, which we wil> call 
A, and that we apply the aggregation B to it, and we find a certain effect x to 
spring up; we then in like coniition^ apply to A, or to a simile of A. the ag- 
gregation C, and flndeitherno effect or the effect y, then it is certain, A and A 



20 

being homon or inter se similia in every respect, that the causal gregarium of x 
existing in b has no simile existing in C, i. e., that each of the gregaria of c 
and the causal gregarium of x existing in B are inter se differentia. Suppose 
then, that we can discover in B the gregaria a, b, c and d, for instance, and 
that we can also discover the gregaria a, b, c and d, in 0, then we know that 
neither a simile of a, nor of b, nor of c, nor of d, was the causal gregarium, 
in B or in similia of B, of x, which sprung from the homonical time and 
place of A and B. And letting the capitals A, B, C, D, &c, be names to dis- 
tinguish aggregations inter se, and the small letters, a, b, c, d, &c, be names 
to distinguish effects inter se, we may make the following tables to assist the 
understanding. 

1st. 2d. 

A and B produce a B and A produce a 

A and C produce b B and C produce g 

■A and D produce c B and D produce h 

A and E produce d B and E produce i 

A and F produce e B and F prod vice j 

A and G produce f &c. B and G produce k &c. 

Now in the first set of instances in the homonical time and ?>lace of 
the effects, if we desire to find the causal gregaria of a, which exist in B, 
we see that gregaria, similical with the causal gregaria in B of the effect a, 
do not exist in C, nor D, nor E, &c, and hence wherever we find a gregarium 
in C, D, E &c, which has a simile in B, we know that this similical grega- 
rium in B and the causal gregarium, or each of the causal gregaria in B, if 
there should be more than one causal gregarium in B, are inter se differentia. 
And in the second set of instances we may deal in like manner with the gre- 
garia of A. And after that we have differentiated, by differential induction, 
as in the manner now 7 explained above, the gregaria in B, which are not the 
causal gregaria, from the causal gregaria, we may dismiss the non causal gre- 
garia from our consideration and look further into the matter. 

The case, however, may and does occur in chemistry, where two ag- 
gregations will not produce an effect without a third aggregation being 
brought to bear upon them, and then differential induction is rendered still 
more complicated and difficult. Suppose that A, B and C, produce the effect 
a, and that A and B produce b, A and C produce c, and B and C produce d, 
then it is evident that the causal gregaria of a existing in A and each of the 
gregaria in B are differentia; for, if the causal giegaria of a in A, have simi- 
lia in B, then B and C would produce a without A. And in like manner, it 
is evident that the causal gregaria of a in A. and each of the gregaria in C 
are differentia, and the causal gregaria of a in B and each 'of the gregaria 
in A are differentia, and the causal gregaria of a in B and each of the gre 



21 

garia in C are differentia. And hence the proximate causal gregaria 
of a must be in b and C, or in c and B, or in d and A. Now if A and B really 
produce no effect at all, and if B and C produce no effect at all, it is evident 
that tne proximate causal gregaria are in c and B. And if c be a permanent 
effect, we may then deal with c and with B in the manner above given ; but 
if c be evanescent we are not able to manage it in that manner. If nitric 
acid and platinum in an homonical time and place produce no effect, and if 
silver and platinum in like conditions produce no effect, but nitric acid dis- 
olve silver, i. e., nitric acid and silver produce an effect, which we will call c; 
and if nitric acid, silver and platinum produce an effect, which we will call 

a, then it is evident that the causal gregaria of a lie in c and platinum, and 
we must, if possible, inquire into the gregaria of c and also into those of 
platinum by differential induction as explained above. 

But suppose, as before, that A, B aud C produce the effect a, and that 
A and B actually produce b, and A and C produce c, and B and C produce d, 
it is then uncertain whether b and C, c and B, or d and A produce a; and if 
the effects, b, c, and d be evanescent and not of a permanent character perse, 
so that we cannot examine them, we can make no inductions respecting the 
proximate causal gregaria of a. If, however, b, c and d be of a permanent, 
character, when A and B have produced b, we can try b with C, and &o of c 
and d; and in this manner we can differentiate the gregaria of c and d from 
the causal gregaria of a. 

When four elements enter into a compound in a binary manner, diff- 
erential induction is eas}^ When A and B produce a, and C and D produce 

b, and if a and b be permanent effects and they produce c, we may first make 
differential inductions of the causal gregaria of a in A, and in B, of b in C 
and in D, and then of the causal gregdria of c in a and in b. But ic may b^ 
that A, B, C and D contain the still more remote causal gregaria of a; A and 
B may produce b, A and produce c, B and C produce f, or the operation 
may be still more complicated and then tii -;*e resultant effects produce their 
effects and the last mentioned effects produee still others, and so on to a 
given effect x for instance. Organic and animal life is, no doubt, produced 
in this manner. But however complicated the matter may be, the principle 
of differential induction in any case has a simile in every other case, and it 
may be summed up in the following differential proposition; whatever gre- 
garia being put in the conditions, in which certain causal gregaria produce a 
given effect, and the}' do not produce a simile of that effect and the causal 
gregaria of that effect are differentia. 

CHAPTER VII. 

S1MILICAL INDUCTION. 

Having treated in the preceeding chapter of differential induction 
we will not find much difficulty in understanding similical induction, and we 



22 

need not spend much time upon the subject. But in order to assist the un- 
derstanding let us represent aggregations by the capitals A, B, C, &c, and 
their effects by the small letters a,b, c &c, and let us form two tables as before: 

1st. 2d. 

A and B produce a B and A produce a 

A and C produce a B and G produce a 

A and D produce a, &c. B and H produce a, &c. 

Now in the first set of instances, as B, G and D, each of them along 
with A produce a, A remaining the same or a similie of A being in each 
instance, the respect, in which B, C and D are inter se si-milia, is the causal 
gregarium of a, existing in B, in C and in D, &c. ; and in the second set the 
respect in which A, G and H are inter se similia, is the causal gregarium of 
a existing in A. And if A and B produce cl, and then d and C produce a, 
we may make a similical induction respecting the causal gregaria in d and 
in C in the manner shown above. And if A and B produce d, and C and D 
produce g, and then d and g produce a, we may continue our inductions in 
like manner, and so on. 

In differential induction the respect in which aggregations, one of 
which contains causal gregaria of a given effect and the others not, are inter 
se similia, and the causal gregarium in the one causal aggregation are inter 
se differentia; in similical induction, the respect in which aggregations, all 
uf which contain causal gregaria of a given effect, are inter se similia, and 
the causal gregarium of the given effect in any one of the aggregations com 
pared are inter se similia. And if two aggregations containing causal gre- 
garia of a gi^en effect and compared in the manner above sUtecl by infer se 
similia onty in one respect, that respect is the causal gregarium of the effect 
existing in each of the aggregations. The principle of similical induction 
may be summed up in the following similical proposition ; whatever gregaria 
in similical conditions produce similical effects, are inter se similia. 

CHAPTER VIII. 

INCOMMENSUKAL INDUCTION. 

We have seen heretofore that, commensura and incommensura are 
relations which have an homonical standard, and therefore when these terms 
are applied to aggregate existences, or to gregaria. they arc applicable only to 
those existences, which are inter se similia. Thus: a may be equal to a', i.e., 
a=a\ or a^a', a and a' being inter se similia; but if a and b be inter se cliff 
erentia, a cannot be equal to b, i. e., a=b, and a< b, are propositions without 
any meaning, just as much as when we say that this sound is equal to that 
color. Now all inconimensur&l effects are inter se incommensura, by reason 
of the incommensural relations of time or of space or of both, existing be- 
tween the aggregation in which the effect is grounded and the other aggre- 
gation containing causal gregaria; or else by reason of the incommensural 






23 

relations between the quantities of the causal gregaria at homonical or heteri- 
cal times, the times of application remaining commensura, and the spaces 
between the aggregations remaining commensura. Thus; an hour and a day 
are incommensural relations of time, and a steady rain for one hour and a 
steady rain for one day leave incommensural effects grounded in the land 
from the incommensural relations of their times, the quantities of rain falling 
in commensural times being commensura. And it is evident that, in heteri- 
cal iustauts of time the causes of the effects grounded in the land, the rain 
which falls, are not homonical but similical; yet commensural quantities 
falling in commensural times, the effects will be incommensura 
from the incommensural relations of the times of the similical 
causal gregaria in operation to produce the sums total of the effects. Again; 
in the radiation of influences, the effects of those influences will be inter se 
incommensura from incommensural relations of space, the times, and quan- 
tities of gregaria in aggregations, in which the effects are grounded, being 
inter se commensura. Thus: 




If A be a body radiating heat, for instance, a body at a will receive, in 
commensural times, more of the radiated influence than a similar and com- 
mensural body at b, i. e., the effect grounded in the body at a and the effect 
grounded in the body at b will be incommensura. A<«-ain : 



B 



o 

/ 



If there be two pieces of iron, whose weights are inter se commensura, 
attached to the lever A 0, the one at B and the other at C. their forces exerted 
upon a body at A will be inter se incommensura from their incommensurai 
relations of space from the fulcrum. And again ; if in commensural relation 
of time and space, incommensural quantities exert their influences, the effects 
will be incommensura. 

And we must bear in mind that the incommensural effects, which are 
to be the subjects of incomme.isural induction, are grounded, and witnessed 
by our senses, in one of the aggregations containing causal gregaria, and our 
object is to And the other aggregation or aggregations containing the re- 
maining causal gregaria. Thus; if A and B at one time produce a, and at a 



24 

other time A and B produce a', and a<a', these incommensural effects are 
grounded and witnessed by our senses, either in A or in B. When oxygen 
supports the combustion of eoal, the effect, which our senses witness,, is 
grounded in the coal. Now it is evident that, if A and B produce no effect 
whatever upon each other, they cannot produce incommensural effects : If A 
or B incommensurate a, A or B must be an aggregation containing causal 
gregaria. And hence, letting B be the name of similical aggregations, if we 
find the similical effects, named a, grounded in B, and these effects be inter 
se incommensura, we may then look for some other aggregation, A for in- 
stance, aiad make observations or try experiments with A and B, and by in- 
commensural induction determine whether or not A c@ntain causal gregaria 
of a. Thus; commencing with incommensural relations of space, suppose 
the effect a grounded in B to be inconimensurated when B approaches or 
receeds from A; if now the position of A in relation to other aggregations 
be changed, i. e., if the other aggregations among which A is situated, be 
heterated by changing the position of A or of B, and a be i icomniensurated 
when B approaches or receeds from A, then it is evident that A contains 
causal gregaria ot a. That the earth contains causal gregaria of the gravi- 
tation ®f terrestrial bodies towards its center is evident by incommensural 
induction. On the opposite sides of the earth at the same time, vvIdu the 
same stars contain between them and the earth one set of terrestrial bodies 
and the earth is between those stars and an other set of terrestrial bodies, the 
gravities or effects grounded in both sets of bodies become incommensura at 
incommensural distances from the earth's surface. 

In the foregoing example we have seen that, fiom the incommensural 
relations of space between aggregations containing causal gregaria incom- 
mensural effects arise. Incommensural quantities or intensities of causal 
gregaria, their times and spaces remaining commensura, produce also incom- 
mensural effects. If a barometer be placed under the receiver of an air- 
pump, and the quantity of air be increased and again diminished, and such 
incommensural quantities be attended with incommensural effects upon the 
barometer and the influence of all other objects be heterated from the 
homonical time and place of the effects, it is evident that the pressure of the 
atmosphere is the cause of such effects. And hence when effects grounded in 
certain aggregations are inconimensurated and we can perceive by observa- 
tion, and still more when we can we can make the experiment, that the quan- 
tities or intensities of gregaria in some other aggregation are corellativety 
incommensura, and we can also heterate other objects, we may be assured 
that the correlative incommensura are connected with the effects by 
causation. 

And again: the relations of time may enable us to make incommen- 
sural induction of the cauees of incommensural effects. Al though we can 



25 

not in one day or in one year perceive any material change in the falls of 
Niagara, yet other objects being heterated, and the water continuing to flow 
over from year to year and very gradual changes continuing to take place 
and being incommensura in incommensural times, other things being equal, 
from the incommensural relations of the times of the flowing and of the 
wearing away of the rock, we can infer the water to contain causal gregaria, 
in the absence of other experience. 

The principle of incommensural induction may be stated in the fol- 
lowing incommensural propositions: The relations of the times ©f causal 
gregaria to incommenBural effects, spaces and quantities being commensura, 
are incommensura; the relations of the spaces of causal gregaria to incom- 
mensural effects, times and quantities being commensura, are incommensura; 
and the relations of quantities of causal gregaria to incommensural effects, 
times and spaces being commensura, are incommensura. 

CHAPTER IX. 

COMMENSURAL INDUCTION. 

We have seen in the previous chapter that, incommensural effects, timet 
being commensura, depend upon incommensural relations of spaces or of quan- 
tities between the eausal gregaria; and, on the other hand, eommensural 
effects, whose times are commensura, depend upon eommensural relations of 
quantities or of spaces between the causal gregaria. And we must always 
bear in mind that, not an homonical gregarium but heterical gregaria are 
the causes of all effects, and that some of the causal gregaria are contained 
in the aggregation in which our senses witness the effect grounded, and some 
ot them in some other aggregation, for which we are seeking as the cause of 
the phenomenon, when a magnet attracts iron-filings, some of the causal 
gregaria are in the magnet and others in the filings. And it is quite evident that, 
if we represent the quantity of the causal gregaria existing in a certain magnet 
by A, and the quantity existing in a certain piece of iron by b, and the iron of 
the weight c be attracted through a certain space A in the time d, a magnet 
containing 2a will attract iron containing 2b and of the weight 2c through 
the space A in the time d. If twelve pounds weight attached by a cord will 
raise twenty pounds upon an inclined plane through the space A in the time 
d, twenty-four pounds in like manner will raise forty pounds. And as in 
incommensural so in eommensural induction, we must look to the relations 
of the effects, which we witness, and then to the relations of times spaces and 
quantities of other aggregations to these effects. And we have already re- 
marked that, neither incommensural nor eommensural induction has any 
reference to kinds of effects, but that on the contrary the effects, whether they 
be inter se commensura or incommensura, are always inter se similia. 

Suppose then that by observation or experiment we find, first by an 



26 

homonical induction, A and B to produce a in the space b in the time.c, and 
in other parts of space we find a simile of A grounded in a simile of B; we 
we must then look to A or for some simile of A, in the respect of the causal 
gregaria of a existing in A; and in order to determine which object is this 
simile of A, we must examine the quantity of causal gregaria in A and in B, 
and their relations in§B, and also the quantity of gregaria in the simile of B, 
in which we witness the effect, and the relations of this simile of B in space 
with other objects. And if we find an object, which we may call y, whose 
relation to the simile of B in space is commensural with the relation of A to 
B, times and the effects, A and a' being commensura, so far y is indicated as 
containing causal gregaria of a'. And if now by a change of spaces we can 
heterate other objects from relations similical with the relations of A to B, 
we can then fairly conclude that y, contains causal gregaria of the effect a'. 
The principle of commensural induction may be summed up in the following 
commensural propositions: The relations ©f space between thfe causal gre- 
garia of commensural effects, times and quantities being commensura, are inter 
se commensura; the relations of quantities of the causal gregaria of com- 
mensural effects, times and spaces being commensura, are inter se commen- 
sura; and the relations of times of the causal gregaria, of commensural 
effects, quantities and spaces being commensura, are inter se commensura. 

CHAPTER X. 

INDUCTION PROMISCUOUSLY. 

From what has been said in the previous chapters in this book, it must 
appear that in making inductions we use for the most part two cases at least, 
in which the aggregations are not homonical hetera, but homonical and 
heterical hetera. Thus: if we wish to make an heterical induction of the 
aggregations A, B and C, which in one instance we find to be in the homoni- 
cal time and place from which spring the effect Z, we look for another in- 
stance of the effect Z, in whose time and place A nor a simile of A is not pres- 
ent: and in this latter instance, we do not find the homonical B and C, but 
we find similical B and C. And hence all induction proceeds upon the truth, 
that the laws of nature are uniform, or that similical or commensural causes 
in like conditions always produce similical or commensural results: and this 
truth, as we have seen heretofore, is established in our minds by the homoni- 
cal syllogism. And in order to make even heterical inductions, we must have 
experience gained by observation or experiment, and this experience depends 
upon the powers of the mind to recognize homon, hetera, similia, differentia, 
commensura and incommensura. We find by experience, for instance, that a 
certain piece ot soap will not cleanse any object, with which it does not come in 
contact; and if now we call this certain piece A, by the homonical syllogism) 
a simile of A will be conditioned in a similar manner: and hence if we find 



27 
an instance of cleansing in whose place a simile of A was not present, we 
make the heterical induction that A is not the cause of cleansing in this in- 
stance, and not a sine qua non of such effects. Heterical induction of aggre- 
gations, indeed, goes no farther than the particular instance from which a 
certain aggregation has been heterated. If, for instance, A, B and C are the 
only aggregations present when the effect Z comes into existence, and sup- 
posing A to have been a cause of Z, in this particular instance, we know by 
heterical induction, that R was not a cause of the homonical Z, but for all 
that we do not know that R, if in the place of A, would not be a cause of a 
similical Z. For the causal gregaria existing in A may have similical gre- 
garia existing in R, and hence R would also be a cause o! such effects as Z- 
Heterical induction of aggregations does no more than remove from an in- 
stance of a certain effect, certain aggregations as sine quibus non, and thus 
clear the way for further investigation. 

Homonical induction proves directly causation in the instance to which 
it is applied; but the homonical induction of aggregations, al thought it prove 
a certain aggregation to be a sine qua non of a particular effect, yet it does 
not prove similical aggregations to be sine quibus non of effects similical 
with that particular one. Thus, if we find the aggregations, A, B and C in 
the time and place from which spring the effect Z, and by observation or ex- 
periment we find B and C without A in a similical time and place, and no 
effect follows, we can conclude that A was a sine qua non of that homonical 
Z, but we can not conclude that similia of A are sine quibus non of similia 
of Z. For although A and D as aggregations may be differentia, yet the 
causal gregaria of homonical Z existing in A may have similical gregaria 
in D; and hence D also will contain causal gregaria of similia of Z. Arsenic, 
copper and lead, as aggregations, are inter se differentia, yet in some respects 
they all contain similical gregaria, and hence each of them is a poison. And 
though by homonical induction of aggregations we prove a cause of simili- 
cal effects, yet we do not prove the only cause. But if we can make an ho- 
monical induction of gregaria, we will prove the only causes of similical 
effects. Ic is very seldom, nowever, that we are able to obtain the data, either 
b} T observation or experiment, from which we can make an homonical induc- 
tion of gregaria, and in order to make inductions of gregaria we are obliged 
to resort to differential and similical inductions. 

In differential induction, which presupposes homonical induction of 
aggregations, we look directly at the gregaria of aggregations, and having 
applied these aggregations severally to a common substance, or to substances 
entirely similia inter se, we note the gregaria, which are inter se similia in 
two substances, one of which along with the substance A for instance, will 
produce the effect Z, while the other along with the substance A will not pro- 
duce a simile of Z, and then we differentiate those similia from the causal 



28 
gregaria. Sugar and soda, for instance, will both dissolve in pure water, 
these capacial gregaria of the two substances are inter se similia; but when 
vinegar is applied to soda it will foam and boil, while when applied to sugar 
it will not; the capacial gregarium of being held in solution, therefore, is not 
in soda the cause of the ebulition witnessed when it is put into acid. In the 
first. book of this volume we spoke of facial and capacial gregaria; we called 
the color, the taste, the feeling, the smell and the sound of objects, their facial 
gregaria, because they present such appearances to our senses. In reality, 
however, all these things are capacial gregaria ; and the only difference is, 
that facial gregaria are perceptional facts immediately noticed by the mind, 
while our knowledge of what we have called capacial gregaria is derived 
from a comparison of perceptional facts. Thus, if I apply sugar to my 
tongue an effect is produced immediately between the sugar and my organs 
of taste ; but if I put a lump of sugar in water, 1 see the sugar and the water 
and I may see the sugar dissolving; I, indeed, make an induction in every 
instance to arrive at the knowledge of capacial gregaria of aggregations. 
Now in making differential iuductions, we always arrive at the knowledge of 
similical gregaria in various substances by observing the facts which spring 
from them when applied to similical substances. Thus, supposing our or- 
gans of taste to remain in similical conditions during a certain time, and 
during this time we taste two substances and rind their tastes to be exactly 
alike: if now we find the one when taken into the stomach will act as an 
emetic and the other as a cathartic, we feel assured that the qualities, the 
gregaria which are similia in regard to our taste, and the gregaria, which 
produce in the stomach differential effects, must be inter se differentia. And 
so we may try any two or more substances with pure water or with any other 
thing, and in this manner determine similical gregar ial, and if then we apply 
these substances to some other thing and find differential effects, we may 
differentiate the similical gregaria from the causal gregaria of a given effect. 
Differential induction does not, indeed, determine what gregaria are causal 
gregaria, but it merely determines what gregaria are not causal gregaria. 
And this it does not only in respect to a particular instance 
but in respect to all instances of similical effects. In the compli- 
cated workings of nature, however, laws are frequently antagonistic, 
and when one prevails over another, the prevailing one must always be 
considered the cause of the ensuing change which takes place, while the 
abrogated law, as it were, is not the cause although it is often called so. And 
in order to make the subjects of differential and similical induction clear, it 
is necessary to speak of this matter here. If, for instance, two men with 
rope and pullies be raising a rock and the rope break and the rock fall to the 
ground, we are apt to say that the breaking of the rope is the cause of the 
rock's falling, while in truth the causal gregaria of the rock's falling are in 



29 

the earth and rock, and the rope has nothing to do with it; though the rope, 
before it broke, was a cause of the rocks rising. Every change, indeed, is an 
effect, and when a certain positive phenomenon is going on it is being or has 
been produced by certain causes, some of which may cease to act and then the 
phenomenon disappears, in which case we are accustomed to call the cessa- 
tion of the cause of its production, the cause of its disappearance. We are 
accustomed to say that the want of water is the cause of the death of a fish 
up on the land. That, however, which is heterated, the absence of a thing 
the want of an aggregation or gregarium, can not be the cause of anything. 
Certain laws may be kept in operation by certain gregaria of aggregations 
and then certain phenomena exist; take away one of the aggregations, the 
taking away of which is truly an effect, and although we may properly call 
this taking away of the aggregation the reason of the cessation of the phe- 
nomenon, yet it is not the cause of such cessation. That only which acts 
can be a cause. And hence although there may be and is plurality of causes 
of similical effects, i. e., the causes of similical effects are hetera, yet siinili- 
cal effects can not be produced by differential causes. And hence, although 
many aggregations, which as aggregations are inter se differentia, may pro- 
duce eimilica] effects, yet ;vhen we come to the causal gregaria of similical 
effects, the causal gregaria will alwa} r s be similical. And therefore, the 
causal gregaria of similical effects being inter se similical, we at once know 
that, of two aggregations, one of which produces the effect and the other not, 
the gregaria which are inter se similia and the causal gregaria are inter se 
differentia. 

In similical induction we compare together different aggregations, 
each of which we find to c©ntain causal gregaria of similical effects to ascer- 
tain in what they agree. And if they agree but in one respect, this respect 
we know must be a causal gregarium: for the causes of similical effects are 
inter se similia If they agree in several respects, we can not tell which of 
the similia are causal gregaria, and we should try by differential induction 
to differentiate some of these similia from the causal gregaria. Thus: if A, 
B, C and D will, each of them, with G produce similical effects, and if they 
all agree in several respects so that we can not tell the causal gregarium in 
either of them, we may find an aggregregation in which some of the gregaria 
existing as similia in A, B, C and D, exist also, and yet the aggregation along 
with G will not produce the effect. That crystaline structure is not the 
causal gregarium of the double refraction of light is clearly proven by differ- 
ential induction, although all substances which have hitherto been found to 
cause the double refraction of light, have been crystaline; and therefore, if 
we knew that they did not agree in any other respect, by similical induction, 
it would be proven, that double refraction depended upon crystaline structure 
alone. Crystaline structure may, indeed, be one of the causal gregaria exist- 



30 

ing in all substances, which refract light in this manner; but it is either not 
a cause at all, or at best it is not of itself the cause, since all crystaline sub- 
stances do not cause double refraction. Differential and similical inductions 
' aid each other in the search after causes, and neither of them should be ne- 
glected in any case, if they can be applied. 

Incommensural and commensurai inductions also aid each other in 
science. That the oscilations of the pendulum are caused by the earth, i. e., 
that the earth contains causal gregaria of these oscilations, and also that the 
earth contains causal gregaria of the gravity of terestrial objects, was proven 
by incommensural induction ; and then Newton by commensurai induction 
proved the earth to contain also causal gregaria of the motion ©f the moon, 
and established what is called the universal law of gravitation. It does not 
seem to me to be necessary to speak farther upon the six methods of making 
inductions which we have endeavored to exhibit in the previous pages. 
These six methods of induction with the aid of ratiocination exhaust the 
powers of the human mind in drawing logical conclusions. And while 
treating of our subject in the first book, we saw that hetera lie at the founda- 
tions ©f knowledge and that homon is at the foundation of propositions; and 
we must now see that homon is at the foundation of all induction and that 
the homonical syllogism, sustains the truths upon which every induction 
proceeds. 

But before passing on to further considerations it seems necessary to 
make a few remarks upon the methods of induction which have been set out 
by J. Stuart Mill, and in doing so we will not go into a lengthy discussion, 
as we believe that the student who has mastered the preceding pages of this 
book, will be able with but few suggestions, to perceive, what we consider, 
the errors of Mr. Mill. Of Mr. Mill's method of Residues, we shall merely 
remark that when we have subducted from any phenomena, what by previ- 
ous inductions and ratiocinations we already know to be due to known 
causes, we proceed with the residue by some one or other of the six methods, 
which we have given, and that there is nothing peculiar to his method of 
residues, so that it should be considered in itself a particular kind ©f 
induction. 

In what Mr. Mill calls the method of agreement there is the mixing 
together and confounding of what we have called heterical induction with 
similical induction. The axiom upon which Mr. Mill considers this method 
to rest, to-wit: "Whatever circumstances can be excluded, without prejudice 
to the phenomenon, or can be absent notwithstanding its presence, is not con- 
nected with it in the way of causation, " is applicable only to heterical induc- 
tion, yet Mr. Mill endeavors to apply his method of agreement to infer caus- 
ation from the agreement in respect to the presence of some antecedent in 



31 
every case from which the effect arises, which can be done only by similical 
induction. 

Mr. MilPs method of Difference corresponds with what we have called 
homonical inductions, though his exposition of it has not been satisfactory 
to our mind. What Mr. Mill calls the Joint Method of Agreement and 
Difference, we regard as an intermixture of homonical induction with erro- 
neous views, which indeed, have reference to differential induction, although 
Mr. Mill had no conception of such method. It is, indeed, quite evident, 
that if A will produce a certain effect and B will not, the causal gregaria ex- 
isting in A have no similia existing in B, and if now we could examine every 
substance which will not produce the given effect and find that they all 
agree in not containing some gregarium which is contained by A, there 
would be a strong probability, and nothing more than a probability, that this 
gregarium was a cause of the given effect. To pursue such a method, how- 
ever, would be to depart from true induction and in the labyrinths of nature 
it is entirely impractical, and of very little value could it be done. On the 
other hand if we have but two cases, in one of which the effect springs from 
A, B and C, while in the other, viz : A and B, the effect will not be pro- 
duced, although we may never be able by experiment to remove and again 
replace C, yet the two cases furnish all the data necessary for making the 
homonical induction that C contains causal gregaria of the effect. We con- 
clude that there is nothing in Mr. Mill's Joiut Method to make it a particu- 
lar kind of induction and further that a great part of his doctrine respect- 
ing it is erroneous. 

Of Mr. Mill's method of concomttant variations, we will only say that 
he does not make any reference to what we consider to be the true principles 
involved in the matter, but treats of cases, some of which are to be deter- 
mined by commensural and others by incommensural induction. 

We have been very limited in our remarks upon the methods of Mr. 
Mill, as we desire in this book to take the affirmative and not the negative 
side of questions. Our object is to build up and not to tear down. And we 
propose also to make this book as concise as possible and not fill and enlarge 
it with criticisms. We may dismiss the subject of the inductive methods 
here, hoping that the reader will be able to understand the matter. 

CHAPTER XI. 

HYPOTHESES. 

In the previous pages, we have dealt only with those principles which 
are brought into view by the comparisons of truths which have been derived 
from actual facts. And in the investigation of nature, our object must always 
be to find out what actually exists and how it operates, and not to assume 
certain hypotheses and from them determine how nature should exist and 



32 

operate. He, who would gain any scientific knowledge of the phenomena of 
nature, must investigate and not make assumptions. When we have really 
gained any new truth in nature, we do not rest the evidence of that truth 
upon an hppothesis; but in regard to all certain knowledge, we apply the 
saying of Newton "Hypotheses non fingo." Yet it is natural for man to 
form theories, and these theories often direct his energies towards valuable 
results. And for the purpose of stimulating the mind to investigation an 
hypothesis may be laid clown, and in many instances for that purpose an hy- 
pothesis must be resorted to. No man, whose object is to search after truth, 
will take the trouble of investigating anj^thing unless he expects to find out 
whether something which he has in view be true or not. A scientific 
hypothesis, therefore, is a subject stated for debate, in which arguments pro 
and con can be brought from actual facts in nature. If by ratiocination and 
induction founded upon actual phenomena, the hypothesis can be proven, 
that closes the debate and the hypothesis is converted into a truth, the evi- 
dence of which does not at all rest upon the hopothesis. And hence when 
we have laid down an hypothesis, our object must be to prove or disprove it 
from actual phenomena. But from nature we can prove only horn on or 
homa, hetera, similia, differentia, commensura and incomensura; and there- 
fore, scientific hypotheses may be divided into homonical, hetera, similical, 
differential, commensural and incommensural hypotheses. 

In heterical hypotheses, which seem to be the most convenient to be 
treated of first in order, we may make a supposition respecting the heterical 
existences of a phenomenon; or granting its homonical existence, we may 
lay down an heterical hypothesis respecting its causal grescaria as sine quibus 
non of certain effects. Thus: as a simple example of a supposition respect- 
ing the heterical existence of a phenomenon ; suppose we see a certain horse 
in an enclosure to-day, and to-morrow we see a horse in another place so 
much like the former that we are uncertain whether it be the same horse 
which we first saw, we may make the heterical hypothesis that, it was not the 
same ons, i. e., this horse and the one we first saw are hetera, and then we 
must look for the evidence to prove the hopothesis. And if by investigation 
we find that the first horse has been continuously and is now in the same en- 
closure, we have proven the l^pothesis to be a truth, whose evidence does not 
rest upon an hypothesis, but upon actual relations of time and space. And 
a similar example might be given to illustrate homonical hypotheses respect- 
ing the homonical existence of a phenomenon: we need not, therefore, speak 
of this again under the head of homonical hypotheses. But suppositions re- 
specting the causes of phenomena are also useful to excite endeavors, and we 
may make heterical hypotheses respecting causation. If the aggregations 
A, B, C and D be in the homonical time and place from which springs the 
effect R, we may suppose, for instance, that D is not a sine qua non of the 



33 

II ; and to prove our hypothesis we find another instance of the effect R, 
from which D was absent in time or space. And again : respecting causal 
gregaria, if the aggregation A along with Z will produce a given effect, and 
Balso along with Z will produce a similar effect, and we can perceive that A 
possesses gregaria, which B does not, we may heterate those gregaria con- 
tained by A, but not by B, from the causal gregaria of tha effect produced by 
A and Z, and thus prove the heterical hypothesis respecting those gregaria, 
if we have made one. And we have already, no doubt, gone far enough to 
see that heterical hypotheses, respecting the existence of any phenomenon, 
to be worth anything, must be susceptable of proof by simple heteration, and 
that heterical hypotheses respecting causation must be proven by heterical 
induction. 

Homonial hypotheses also respecting causation must be proven by 
homonical induction; and until they are so proven, they are not, of course, 
to be received as really true, however useful they may be in stimulating in- 
quiry. Homonical inductions-, indeed, are best and more frequently made by 
experiments than by observations upon nature in her undisturbed processes 
offered gratuitously to our senses, and therefore we would more frequently 
resort to experiments to prove any homonical hypothesis. If, for instance, we 
should suppose that, it is the equal pressure of the atmosphere upon un- 
equally balanced columns of water, which force the water up the shorter arm 
of a s3*phon, w T e could make experiments from which an homonical induction 
of the real cause could be brought out and the hypothesis proven. That there 
is an ether pervading all space and causing light by its vibrations, however, 
can not be proven by homonical induction, aud if ever proven, (and without 
being proven the hypothesis amounts to nothing) it must be proven by simil- 
ical induction. An homonical induction can not be made in any case, unless 
the existence of aggregations containg causal gregaria can first be proven, 
If, for instance, we suppose that the aggregations A, B and C, produce x, 
when we do not know, whether or not, A really has an existence, we can 
make no homonical induction in the case; for although we should find that 
B and C alone will not produce x, that is no evidence of the agency or exis- 
tence of A in the former case Homonical hypotheses respecting causation, 
to be useful in increasing our stock of knowledge, must be susceptible of 
proof by homonical induction. And no hypotheses respecting the existence 
of an aggregation containing causal gregaria can be thus proven. 

We may also make differential hypotheses respecting causal gregaria, 
and for their proof we must resort to differential Induction. We might sup- 
pose, for instance, that the quality of dissolving upon the tongue and the 
causal gregaria of the taste in common salt are differentia; and by examin- 
ing other substances containing this quality, we could prove our hypothesis. 
And in the examination of nature, as differential inductions, though they do 



34 

not prove what the causal gregaria are, assist very much in making similical 
inductions, so differential hypotheses should be assumed and tried that we 
may have every help in unravelling natures complications. 

In similical hypotheses we assume that, the causal gregaria of certain 
phenomena, whose causes we wish to ascertain, and the gregaria of certain 
objects, with which we are familiar, are similia: and if their effects can be 
shown to be inter se similia, we prove the hypothesis. Thus; if we find a 
particular color upon white paper, we may assume that the aggregation 
whatever it might have been, containing causal gregaria of such effect, was 
similar, in respect to its causal gregaria, to some object with which we are, 
familiar; and if the object with which we are familiar will produce upon the 
same kind of paper the same kind of color, we prove the hypothsis. If all 
the planets contain the quality of attracting iron, they, each of them, possess 
gregaria similar to the lode stone. And if we could make ourselves certain 
of the existence in any place, of an ether, whose vibrations would produce 
light, we could prove the ethereal hypothesis. 

Respecting incommensural effects, we may make three suppositions, 
viz: first, that the times and spaces being commensura, th© increase of the 
quantity of gregaria in a certain object incommensurates the effects; second, 
that times and quantities being commensura, the incommensural effects de- 
pend upon incommensural relations of space; and third, that spaces and 
quantities being commensura, the incommensural effects depend upon incom- 
mensural relations of time. And having made our hypothesis, we must then 
find the proof by looking into circumstances varied in these respects, and in 
which the effects occurs. But in making our hypotheses, these hypotheses 
must have reference only to what object or objects contain causal gregaria of 
the incommensural effects, which we witness. And we have remarked 
several times already that, in the cases from which an incommensural induc- 
tion can be made, we are to deal only with similia, commensura and incem- 
mensura being relations inter similia. And the hypotheses above spoken 
of must be proven by incommensural induction. After having ascertained 
that certain objects contain causal gregaria of given effects, we may make 
hypotheses respecting the relative increase or decrease of the effects to the 
times, spaces or quantities of causal gregaria. But these hypotheses can not 
be verified by induction, and unless they can be verified by mathematical 
calculations, they are merely guesses. We are frequently obliged to make 
mathematical calculations respecting the laws of variation in the effects de- 
pending upon incommensural spaces and times. That gravity varies inversly 
as the square of the distance is not an induction, but a truth found out by the 
application of mathematics to actual phenomena. That the spaces passed 
over in successive commensural times by falling bodies are in the relation of 
tho odd numbers 1, 3, 5, 7, &c, is a truth of the same kind, i. e., it is found 



35 

by making calculations of what actually oceurs, as observed, in this respect, 
when bodies fall without being impeded. 

Respecting commensural effects, we may make hypotheses in the same 
manner as respecting incommensural effects, and we must seek for the proof 
in like manner. We do not consider it necessary to make further remarks 
upon hypotheses. Every hypothesis respecting causation must be proved by 
induction ; hypotheses respecting the relations of quantities, times and spaces 
are to be dealt with by ratiocination. 

We have now completed our view of ratiocination and induction, so 
tar as we propose to treat of them in common language. And we may well 
consider of what value these speculations may be to the cause of scieace. 
And merely as a speculation we regard the previous pages as not tntirely 
unworthy of study; but we hope yet to show, that practical results of the 
grandest kind may be expected to follow from a knowledge of the principles 
therein set forth. To gather up an exhibit these principles in fornmlae, and 
to apply them to the actual phenomenon of nature will be our object in 
Book III. 



BOOK III. 

CHAPTER I. 

SIGNS IN RATIOCINATION. 

In the two previous books we have examined the foundations of rea- 
soning throughout and have endeavored to explain, by the use of common 
language, what we have considered necessary on the subjects of ratiocination 
and induction. Common language, however, is not the appropriate vehicle 
of recondite science. Without the assistance of symbols, which form a pe- 
culiar language, Algebra, which consists of syllogisms with commensural 
and incommensural propositions, could not have been brought to any great 
perfection. These commensural and incommensural propositions, with the 
syllogisms constructed upon them, however, have been expressed and wrought 
into Algebric formulae, which can be transformed in various ways, and there- 
by unexpected and grand results can be brought to our apprehension. And 
it may be useful to inquire *whether the other four kinds of propositions also 
can not be expressed in symbols and reduced to formulae, which may be 
formed into a complete system of abstract and exact science. That such 
complete system of science may and will be constructed in the future by the 
genius of man, the author of this treatise believes; and it seems to him to 
be not an unworthy undertaking to make a beginning at its construction, 
which may be an incentive to call to the work others of more favored cir- 
cumstances and greater learning. The construction of such system will, 
therefore, be attempted in this book. And we will commence with simple 
propositions. j* y^ 

Let the sign^f stand for an homonical comparison; then, aV\ will be 
equivalent to the proposition in common language, a and a are homon. Let 
the sign V stand for an heterical comparison; then aya will be equivalent to 
the proposition in common language, a and a are hetera. Let the sign || stand 
for a similical comparison; then a|| a, will be equivalent to the proposition 
in common language, a and a are similia. Let the sign H- stand for a differ- 
ential comparison; then ai+b will be equivalent to a and b are differentia- 
Let the sign = stand (as in Algebra) for a commensural comparison; then, 
a=a will mean that a and a are commensura. Let the signs ;> and < stand 
(as in Algebra) for an incommensural comparison: then, a>a, or a<a, will 
mean that a and a are incommeusura. 



2 
Now by the use of the foregoing signs, we can combine the six kinds 
of propositions in all the figures and modes ' of the syllogism. Thus in 
mode 1st: ' w 

a A a or a A a 
II or K- 

a'Aa' or a'Ab 
/.a || a', or .\aR-a'. 

And these syllogisms will be true irrespective of time and space, i.e., if 
aAa or if a\/a, or if a || a, &c. to-day, they alw r ays have been and always will 
be in a like comparison, so far as time and space, as agents, are concerned. 
But before proceeding further, it is necessary to explain the manner in 
wdiich simple gregar.ia of aggregations by the use of signs. Let the first 
large letters of Alphabet, A, B, C, &c, stand for aggregations, and the first 
small letters, a, b, c, &c, for gregaria, then a syllogism in mode 1st may be 
thus constructed: 

a of 'AAb or, a of AAb 
II or, H- 

a of BAb or, a of Bac 
.-.a of A || a of B. or, .-.a of Ah- a of B. 

Now if a stand for the gregarium — color, we may interpet the syllo- 
gism thus : 

Color of AAb or, Color of AAb 
II or, H- 

Colorof BAb or, Color of B Ac 
.-.Color of A || color of B. or, .-.Color of Ah- color of B 

And these signs as above given are sufficient for all the purposes of the 
singular syllogism and of the singular homonical syllogism. 

But for the purposes of the Plural syllogism, w T e wish signs, not only 
to express the comparison between the terms of the propositions but to show- 
also the comparisons between the existences exhibited in each term. And 
for this purpose, we need but combine the signs already given, and reading 
from the left to right, interpret the sign on the left hand as an adjective and 
the succeeding siarn as a noun. The following table will show the use of 



the signs 














t 


Let the 


sign 


, AA, 


indicate homonical noma. 


u 


u 


u 


A V 


u 




u 


hetera. • 


a 


u 


;; 


A II 


li 




u 


similia. 


(< 


<< 


a 


A If 


u 




11 


differentia 


u 


CI 


u 


A": 


u 




u 


commensura. 


u 


u 


u 


A< 


(d 




u 


incommensura. 


u 


u 


(( 


V A 


(( 


net 


eric 


al horn a. 


a 


»l 


i( 


vv 


l( 




a 


hetera. 


a 


a 


u x 


V 1! 


it 






similia. 


u 


(C 


a 


VH- 


u 




(< 


differentia^ 


u 


u 


a 


V- 


ii 




(i 


commensura. 


u 


u 


u 


V< 


(i 




»t 


incommensura. 



Let the 


sign 


, II A indicate similical homa. 


u 


u 


44 


' II V 


4.4 


44 


hetera. 


a 


U 


44 


li II 


f 


44 


similia. 


a 


a 


44 


1! H- 


44 


differentia. 


a 


u 


44 


11 = 


44 


44 


commensura. 


a 


Cl 


44 


II < 


44 


4'. 


incommensura. 




u 


44 


H-A 


44 


differential homa. 


is 


u 


44 


H-V 


44 


44 


hetera. 


u 


14 


44 


H- II 


44 


44 


similia. 


u 


(4 


44 


H-H- 


44 


44 


differentia. 


- u 


44 


44 


fr'= 


44 


44 


commensura. 


a 


44 


44 


H-< 


44 


44 


incommensura. 


a 


44 


44 


= A 


44 


cominensural homa. 


u 


44 


44 


=V 


44 


44 


hetera. 


(C 


44 


44 


= 11 


44 


44 


similia. . 


(( 


44 


44 


--H- 


44 


44 


differentia. 


U 


44 


44 


= ■— 


44 


(4 


commensura. 


ct 


44 


44 


— < 


%4 


44 


incommensura. 


u 


44 


44 


< V 


44 


incommensitral homa. 


u 


tt 


44 


< A 


44 


44 


hetera; 


41 


44 


44 


< 11 


44 


44 


similia. 


u 


44 


44 


< 14- 


44 


44 


differentia. 


li 


44 


44 


< — 


44 


44 


commensura. 


a 


44 


44 


<< 


44 


44 


incommensura. 


The left hand sign 


indicates the 


comparison between the terms of the 


propositions. 


Th 


as ; in 


the 


equation, 


a-j-b=a-|-b, the sign = expresses 



the comparison between a-f-b and a-j-b; but if a=b, then the expression 
a-j-b= =a+b means, not only that we have an equation, but also that the 
existences exhibited on each side of the equation are inter se commensura 
i. e., each existence ©n one side of the equation sign, has a commensura, 
fellow on the same side and on the other side of the signs. 

Now with the foregoing signs, we may from complete syllogisms in all 
the figures and modes. And commencing with the first four kinds of pro- 
positions, let two clots ( ••) indicate that the existences, between which the}^ 
are placed, are merely grouped together by comparison ; and let AB, without 
dots* between 'them mean as in Algebra, and also the signs -\- and — as in Al- 
gebra, and the following paradigms will show the plural syllogism. 

PLURAL SYLLOGISM — PARADIGM 1ST. 



Mode 1st. 
A..B A A A..B 

II II 
CDAAA'B' 
.\A..Bj|CD. 



Mode 2d. 
A..B VV A'..B 

A A 
CDvvi.'B' 
\A..BVVC..D 



Mode 3d. 
B..B || |! B..B' 

A A 
CD. I| ||B..'B' 
.B..B. li || CD. 



Mode 4th. 

A..B.n-1+CD. 
A A 
E..F. H-H-CD. 
•.indefinite. 



Mode 5th. 

A..BAAA\.B' 
A A 
CDVAA'..B' 
,.A..BVACD. 



Mode 6th. 

'A..BAAA' .B 
A A 
CD 11 AA'..B ; 
-.A..Bi| A CD. 



Mode 7th. 

A..BAAA'..B 
A a 
CDh-aAA.B' 
.\A.Bh--aCD. 



Mode 8th. 
A..BVVA..B' 

A A 

CDaVA'..B' 
.A..BVVCD. 



Mode 9th. 

A..BvvB'..B' 
A A 
CD || VA'..B' 
.-.indefinite. 



Mode 10th. 
A..BVVA'..B 

VV 
CDh-VA'..B 
.-.indefinite 



Mode llth. 

A..B|| ||A'..B' 

A' A 
CD A ||A'..B' 
.-.A..BI! !| CD. 



Mode 12th. 
A..B|| ||A'..B' 

A 

CDv HA' 
•.indefinite. 



A 
B' 



Mode 13th. 
A..B|| ||A'..B' 

A A 
CDH- II A ..B 
.-.A..Bh- II CD. 



Mode 14th. 
A..BH- H-CD 
A A 
E.FAH-CD 
.-.A..BH-H-E..F. 



Mode 15th, 
A..Bh-1+CD 

A A 
E..FVH-CD 
.-. indefinite 



Mode 16th. 
A..B|fH-CD 

A A 
E..F|| h^CD 

.••A..BH-H-E..F. 



The first paradigm shows the plural syllogism, with the first four 
kinds of propositions; in the following paradigm the first two and last two 
kinds of propositions will be combined. 

PARADIGM 2D. 



Mode 1st. 

A..BA AA'..B' 

CD aaa.Tb' 

.\A=..BaC..D 



Mode 2d. 
A..BVVA..B' 

A A 
CD VV A..B 
.•.A..BVVCD. 



Mode 3d. 

B..B= = B'..B' 

A A 
CD= =B'..B' 
.-.B..B= =CD 



Mode 4th. 

A..B«C..D 

A A 

E..F<<CD 

'. indefinite. 



Mode 5th. 
A..B A aA'..B' 

CDV/\A'..B' 
.'.A..B V A CD. 


Mode 6th. 

A..BaA A'..B' 

A A 
CD= A A'..B' 

.-.A..B=aC..D. 


Mode 7th. 

A..BAAA..B' 

1 * A 
CD<aA'..B' 

1 .-.a..b<ac..d. 


Mode 8th. 

A..B VVA'..B' 

A A 
CDaV A'..B' 
.-.A..BVVCD. 


Mode 9th. 
A..BYVA'..B' 

CD=V A A'A< 

.'.indefinite. 


Mode 10th. 

A..BVVA'..B' 

A A 
CD<A,A'..B' . 

.-.indefinite 


Mode llth. 
A..B==A'..B' 

A A 
CD A=A'..B ' 
.•.A..B= =CD. 


Mode 12th. 

.\A..B= =rA' .B' 

A A 
C..Dv=A'..B' 
.-.indefinite. 


Mode 13th. 
A..B==A'..B' 

A A 
CD<=A'..B' 
.\A..B<toCD. 


Mode 14th. 
A..B<<CD. 
A A 
E..F A<CD 
.\A..B<<?E.F. 


Mode loth. 
A..B<<CD 
A A 
E..Fv<CD 

.-.indifinite 


Mode 16th. 
A..B<<CD 
A A 
E..F=<CD. 
.\A..B<<E..F. 



Now in mcde 1st, of paradigm 1st, since AaB, the first premise re- 
duces to A\A; aud as CAD and A' AB', the second premise reduces to CA 
A' ; and hence the conclusion will be A [| C. And in mode 1st of paradigm 
2d, for similiar reasons, the conclusion will be A=C. It must also be ob- 
served that, it is their homonical relations inter se in space, w r hich makes A 
A B, while their times heterate. We have already shown heretofore, that the 



.5 . 
homonical A to-day and the homonical A to-morrow have heterical points of 
time, and they may have heterical whehes, one to-clav and another to-mor- 
row. But for the present we will suppose that, the aggregations, with which 
we are about to deal, are in "and continue in a state of absolute rest; then, 
they will not change their wheres in space. Now with the use of the signs 
already adopted, we may bring the relations of time and space into our pro- 
positions and exhibit them along with the aggregations or gregaria. Let T 
stand, not for time, but for times between which there may be a comparison, 
and let 8 stand for spaces in like manner; the, the proposition A A A', in or- 
der to exhibit the relations of limes and spaces may be written thus: 

T.8. 

AAA': 

Which proposition may be put into common language as follows :— 
The homonical A, having an heterical time but an homonical space with A', 
is homonical with A'. And we may state the first premise of the plural syl- 
logism in Mode 1st thus: 

W A A 



T. S. 

A..B/\ Ai',.B'. 
And this proposition may be stated in common language as follows: — 
A and B, whose times are hetera and spaces homon, having heterical times 
but homonical spaces with A' B', whose times are hetera but spaces homon 
are homonical with A' and B'. And with the signs and letters as they are 
now understood, as we hope, the following four propositions may be expressed : 

(1.) (2:j (3.) (4.). 

W A A VV AV VV VA VV V'V 



T. S. T. S. T. S. . T. S. 



A/.BaAA'..B'. A..BA VA'..B'. A..Bv A A'..B\ ■ A..B\/VA'..B\ 

In the above propositions, the times have reference to the temporal re- 
lations between A..B..A' ..B'. and the mind of the thinker, i. e., to the rela- 
tions between the objective aggregations aid tiie subjective conscious truths. 
And we can easily see that a rose blooming on the tree and the tree itself 
have an homonical time; but the rose will fade and pass away, while the 
tree may yet r&maki, and hence the times of the rose's existence and of the 
tree now are hetera. And the times of the aggregations exhibited in the 
above propositions are considered in their relations, not inter se, but to an 
other existence, the consciousness of the ei'-o. But if we consider tho.se 

7 o 



aggregations in their relations of time inter se without any reference to any 
other thing, the above propositions will be reduced to the following: 

(i.j an (mo (iv.) 

A A A V A V A A VV 



T. S. T. S. T S. T. S. 

A. AyB. AVA'. A..BVVA'..B\ 

Now if we reduce the premises in modes 1st in like manner as the 
propositions last above given, we will have: 

(a.) 
\ A A A 

T* S TT S 

1st., premise _J_ 2d. premise . * ' 

A. C. 

And by the comparison of these existences viz., A and C, we must draw 
the conclusion that: 

(b.) (c.) (d.) («.) 

A A A V A A AAAVAA UAUA AAAVaA 

T. S. T. S. T. S. T. S. T. S. T. S. T. S. T. S. T. S. T. S. T. S. T. S. 



|| C. . A H- C. A = C. A ,<or> C. 

The premises in mode 5th reduce as follows: 



(f-) 





. A 
T. 


A 

8. 
_. t 




A. 


A A 

And as _' 




in the first premise and 


A 
are homos i. e., 




A A \ A A a 
T.S. TVS. T. S. 



A A A V A A 

T. S. T. S. T. S. 

C V A. 

\ A 
T 1 S 
_ ' _ in the second premise 

A, 

the comparison betwten C 



A, 



(g.) 



A A A V A A 

T S T S T S 
and A makes the conclusion __ 

A v C. 



The premises in modes 8 reduce as follows: 

(h.) 
A V A A v V ' A v 



1st., premise, T. H. T. S. T. S. 



A..B V V A'..B\ 

A V A v 

fp c T S 

2d, premise , or __ as A..B and CD are 

A'..B\ CD 

00 
A A A V 

A v A a 

homonical hetera, and as T.S. T. S. T. 8. 

A'..B' a V A'..B\ 

A A V V 

A V A V 

therefore the conclusion, T. S. T. S. T. S. 



A..B V V CD. 

Now propositions either (3) or (III) underlies the conclusions in modes 
1, 5, 6 and 7, and proposition either (4) or (IV) underlies the conclusions in 
modes, 2, 8, 4, 8, 9, 10, 11, 12, 13, 14, 15 and 16; for, similia, differentia, corn- 
mensura and incommensura are also hetera. Our knowledge of hetera and 
consequently of homon depends spon time and space; but our knowledge of 
similia, differentia, commensura and incommensura does not depend upon 
time and space, but upon the gregaria of aggregations. And these substrata 
of our knowledge are to be inquired into from other grounds. 

CHAPTER II. 

SIGNS IN INDUCTION. 

In heterical induction of aggregations, we find two or more instances 
of similical effects, and we use one of the instances to eliminate some of the 
aggregations from the sine quibus non in another instance. The aggrega- 
tions of the two or more instances may be synchronous or they may not be« 
An observation mode in the time of Homer, if correctly made, is as valuable 
for one of the instances, as one mat! a to-day, although the aggregations which 
came under observation then, may have passed away into other forms. And 
in making experiments, the times of the experiments are not homon but 
hetera. But the aggregations brought together in any one instance of an cb- 



8 
servation or experiment have homonical times. And when we view ametalic 
globe, for instance, of the diameter of six inches, we consider it as occupy- 
ing an homonical where, though the wheres of its particles be hetera. 
And *o also, if we bring the aggregations A, B, C, D, &c, in contact with 
each/)ther, we may then consider, the result as an aggregation of aggrega- 
tions and as occupying an homonical where. Now if we let the last letters 
of the Alphabet, v, x, y, z, stand for effects, and let the sign U stand for cau - 
sation, then in view of what has been said above, we will have the proposition, 

(1.) 



A A 
T. 8. 


V V 
T. 8. 


A A 
T.S. 


A..B..C..D. 


V V 


A'..B'..C 


n 


V V 
T.S. 


n 


X 


... II ... 


X' 



And as x and x' are similical effects, they can be produced by simili- 
cal hetera and in order to have similical hetera eo nomine etin numero, we 
must dismiss D in the first term from the sine quibus noaof the effect x. We 
may then find another instance and have the proposition: 

(10 



A A 
T.8. 


V V 
T. S. 

V V 

V V 
T 8. 

II 


A \ 
T. S. 


A"..B" 


A..B .0 


x" 


n 

X ' 



And this proposition enables us to heterate C\ The heterical induc- 
tion of gregaria may be represented in the same manner. Take the proposition 

(2.) 

A A V V A A 

T. 8. T.S. T. &. 



A .. B a a . C .. B 



a..b..c..d e..f..g.h a..b..c. e..f..g..h 

n v v n 

T. 8. 
x || x' 



9 

Now as B || B', they will contain a like number of similical gregaria 
and hence by looking at C, d can be eliminated from the causal grega- 
ria in A. 

Homonical induction is Hie reverse of heterical induction. Taka the 
proposition respecting aggregations: 



(3.) 

A A V V A A 

T. 8. T. ft. T. S. 



A..B..C V V B'..C 

U V V U 

T. 6. 

x H- 0, or y. 

Now as we desire to have similical effects, i. e., x and x', they must be 
produced by similical iietera, eo nomine et in numero, and by looking at (lie 
terms, we see that A must be added to the second term, i. e„ that A was a sine 
qua noil of the effect x. 

In differential induction we first clear the way as much as possible by 
heterical induction of gregaria and thew take the proposition: 



(4.) 



A A 
T. B. 


V V 
T. 8. 


A A 
T. 8. 


A. .B 


V V 


C. .B' 


a..b..c..d i.k.&c. 




a..b..e..f i..k..&c 


U 


V V 
T. S. 


H 


x 


H- 


0, or v. 



And now as B j| B', their greTgaria are similical differentia; and if A || 
U, we should have had similical effects; but as the effects are differentia, their 
causal gregaria in A and in C are differentia: and hence the similical grega- 
ria in A and O may be differentiated from the causal gregaria, i. e., a and b 
and the causal gregaria of x in A are differentia. 

Similical induction is the reverse of differential induction; take the 
proposition. 



10 



(5.) 



A A 
T. S. 


V V 
T. S. 


A A 
T. 8. 


A. .B 


v N ' 


C. .B' 


a..b..e..d i..k..&c. 




a..b..c..f i..k.,&c. 


U 


V V 
T. S. 


n 


x 


ii. 


X' 



Now as x || x', they have been produced by similical gregaria, and as 
3 || B', we must find similical gregaria in A and C, and we find a and b in 
both ; therefore these gregaria, or one of them at least is a causal gregarium. 

We must notice, that in our propositions for making heterical and 
homonical inductions, we represent the aggregations by the signs between 
the terms, merely as net era. This must necessarily be the case; for, we are 
eliminating and aggregating hetera by those processes. In differential and 
similical inductions also we must represent the aggregations by the signs, 
merely as hetera. For, if A..B 

If 
X 

and A || B, w T e know by ratiocination that similical similia will produce simi- 
lical effects; and if Ah-B, we know that similical differentia will produce 
similical effects. But in the above inductive propositions, B || B' and Ak-C, 
as aggregations, and we desire- o find in A and C, the respects, the gregaria 
inter se similia and to make an inference respecting them and this can be 
done only by using the heterical signs between the terms. 

In incommensurl induction, there are three cases; 1st, times and spaces 
being commensura, the quantities are incommensura; 2d the times and quan- 
tities being commensura, the spaces are incommensura; 3d the spaces and 
quantities being commensura, the times are incommensura. Let us suppose 
that we witness the effect in B and B', then:' 

(6,) 

= v = v 

A V A V 

T. S. T. S. T. 8. 



A..B < V A'.B 



n v v u 

— T. 8. — 

x < x' 



11 





(7.) 




A V 
T. S. 


- V < v 
T. S. 


A V 

T. 8. 


A..B 


- V 


A'.JB' 


n 


V V 
T. S. 


^ 


x 


:> 


x' 




(8.) 




A V 
T. S. 


< V = V 




.T. S. 


A V 
T. S. 


A.B 


= V 


A'..B 


U 


v V 
T. S. 


U 


x 


<f 


. . ,.x' 



Coramensural induction brings a simile of one of the aggregations, 
which we have determined by incommensural induction to contain causal 
gregaria of a given effect, and some other aggregation, about which we are 
uncertain, into relations commensural with the relations between the aggre- 
gations, which we know to contain causal gregaria -of such effects. And 
these relations are threefold, hence : 

(9.) 

I 

A V ■ - A V 

T. S. T. S. T.8. 



— 


V 


- V 


T. 




s. 


== 




V 




■ V 


V 




T. 


ti. 



A..B ±s V C..B' 

If - V V u 
— T. 8. — 
x « = x' 

Which proposition brings C and B' into commensural relations with 
the relations of A and B, and when that is done we find the commensural 
effect, and hence, as B || B', we conclude that C contains similical gregaria 
with A. If we should take the second term of proposition (8,) as the first 
term of an inductive com mensural proposition we will have: 





(9.) 




= V = V 


A -V 

T. S. 


T. K 


A'..B' 


= \i 



12 



A V 
T. 8. 

C..B" 

u v v u 

T. S. 
x' = ... x" 

If we cannot thus bring the aggregations, which we are investigating, 
into conimensural relations as above, and rind eommensural effects, we may 
yet frequently, by mathematical calculations, find what would be the effect, if 
such eommensural relations were realized; and this will answer the purpose. 

CHAPTER III. 

HETERICAL IVDUCTION APPLIED. 

In the two previous chapters, we have given formulae, which, when 
carefully considered and fixed in the mind, will assist the understanding in 
investigating nature. Observations and experiments must furnish the data 
but the inferences to be drawn from those data must be dictated by a sound 
philosophy. And the formulae, which we have given, will not only aid the 
mind in making proper inferences, but also in looking for the kind of instan- 
ces, from which alone legitimate inferences can be drawn. And in applying 
the foregoing principles, it will not be necessary for us to bring the cases 
noticed into the exact form of the formulae, as the reader, who lias mastered 
the subject, can easily do that for himself. We wish merely to show the 
utility and importance of the subject, b} r illustrations from cases in which 
these principles have led to scientific discoveries, though the investigators, 
perhaps, were entirely ignorant of the processes heretofore explained. And 
it will not be necessary to furnish -many illustrations to show what may be 
expected to follow from a thorough knowledge of these processes by the 
scientific men of the world, who are engaged in the several departments of 
science. Our illustrations may be taken from any department of Knowledge 
for our principles apply to every branch of science. We will commence 
with heterical induction. 

Among all the varieties of material forms, which surround us in the 
world, chemists have been able to find fifty-five elementary substances,!. 
e. Substances whese particles are inter se similia. And from some or other 
of these element, mineral compounds, vegetable organisms and animal or- 
ganizations are produced. Now nature's labratory can be entered, in the 
first instance, only by induction; we cannot commence with the simple ele- 
ments and reason a priori, or a posteriori, without first having made indue- 



13 • 

lions. There is no evidence, about which weal present know anything, to 
establish any belief, that what now are called elements, are really compounds; 
and when we find the number and kinds of elements, which, from any com- 
pound, or organization, we conelude, that we have all the sine qui bus non, 
and because none other are present, i. e., by heterical induction. But be- 
cause a certain number and kinds of elements arc found in certain instances, 
or even in all instances known tons, we are not certain that each one of 
them is a sine qua non of the given effect ; although this false kind or reason- 
ing per enumeration em simpHcem is still employed by writers upon the 
physical sciences. 

In the organizations of animals we rind an animus or life principle, 
vis vitae, and this principle has been said to possess and exert a force sui 
generis upon the elements and to impart to them, when taken into the stom- 
ach, an unusual action. And although this life principle exists in all ani- 
mals, yet the theory respecting its force on the elements (and it is nothing 
but a theory) has recently been disproved in a measure at least in the most 
satisfactory manner by heterical induction. It has been shown that hard 
.boiled albumen and muscular fibre can be dissolved by adding a few drops 
of muriatic acid to a decoction of the stomach of a dead calf, precisely as ill 
the stomach of a living animal. This one instance heterates the vim vitse 
from the sine quibus non, and leaves the stomach t act, upon chemical prin- 
ciples in dissolving the food; and if the known principles of chemical trans- 
formation do not yet sufficiently account for digestion, it must be further in- 
quired into. Physiologists h«*ve also attributed the formation of formic acid, 
oxalic acid, urea &c, in the body to the force of the vis vitse; yet each of 
these can be formed in the labratory of the chemist, and consequently it is 
proved that vis vitse is not a sine qua non. True heterical induction thus 
dispells mystic theories and opens the true road tor inquiry. 

Chemists have contended that vegetable fibre in a state of decay, which 
is called humus, is absorbed by plants ui.d is necessary to their growth; jet 
this humus can be separated by heterical induction. For, although this 
humus is present in most soils, yet "plants thrive," as we are informed fry Dr. 
Leibig, u in powdered charcoal, and may be brought to blossom and bear 
fruit if exposed to ihe influence of the rain and atmosphere; the charcoal 
may be previously heated to redness. Charcoal is the most 'indifferent' and 
most unchangeable substance known ; it, may be kept for centuries without 
change, and is, therefore, not subject to decomposition." Now one such case, 
as just cited from Dr. Leibig, who reasons more philosophically than most 
chemists, completely hetorates the absorption of humus from the sine qnibus 
non. Leibig contends further, that humus merely furnishes carbonic acid 
for the atmosphere surrounding; the roots and stalk of the plant, and that thii 



14 
carbonic acid is a sine qua non. This, however, cannot be proved by heteri- 
cal induction, which is the only subject, that concerns us at present. 

We find that several kinds of opium contain maconic acid, and from 
the examination of such kinds alone without a true philosoph}' by which to 
test nature, we would erroneously conclude macoraie acid to be asine qua non 
of opium ns an anadyue and soporirr.:, but there are other specimens of opium, 
which do not contain a trace of this acid, and yet thfy produce simiiical 
effects. By heierical induction also, yve establish the truth, that volition and 
the mind's command of the nervous apparatus are not sine qui bus non of 
nutrition in animals. For, in those parts of the. body, which have baen para- 
lyzed and whieU, therefore, are destitute of feeling and not subject to the 
minds control, nutrition still proceeds without interruption. Oxygen may 
be condensed into a liquid by pressure, in which state it posses those grega- 
ria, which distinguish a liquid from a gass ; and yet in either state its actions 
;ipon other substances are inter se suHiilis; and those distinguishing gregaria 
some in the mie and some in the other state, can be heterated from the causal 
gregaria (if the effects oi'oxviren. We need not illustrate further. 

CHARTER IV. 

HOMGNICAL INDUCTION APPLIED. 

We have heretofore observed -that 'heierical induction does not 'deter- 
mine .causes, but merely clears the way so that homonieal i> duction can be 
naade more easily applicable to any given case. Now we find that animals 
having lungs respire the atmosphere, and so long as respiration continues, 
(he circulation of tltfc blood and life tmd heat exist, but let respiration be 
prevented and denlh ensues; by homoincai induction, therefore, the atmos- 
pheres one of the causus of life and heat in such animals. And upon ex- 
amination of the atmosphere, we find it to contain frequently carbonic acid, 
water, some earthy matters and oxygen and nitrogen. The earthy matters, 
carbonic acid and water can be removed from the causes of the effects of 
respiration by heierical induction; but if we remove the oxygen, these effects 
immediately cease, and hence it is certain that oxygen is a sine qua non. 
And by heterieal induction we can remove all elements from the sine quibus 
non of the growth of mammalia excepting those contained in milk; for the 
health and growth oi the young may be promoted by milk alone. Now we 
find milk to contain caseine, a compound containing a large proportion of 
nitrogen; sugar of milk, in which there are large quantities of oxygen and 
hydrogen; lactate of soda, phosphate of liaae^ common s;dt and butyric acid. 
Is each of these elements a sine qua non ? A horse may be kept alive upon 
potatoes, in which the quantity of nitrogen is small, but he does not thrive, 
and if deprived of all food containing nitrogen, he dies. Mammalia cannot 
live without a salt, nor can any one of the constituents of milk be wan-ing 



15 
for any great length of time without a marked influence upon the health of 
the animal. Experiments showing such truths furnish the data for homoni- 
cal inductions. Plants cannot grovt it either hydrogen or carbonic acid be 
wanting, and hence, these are site quibus uon. 

And again, we see that if the blood be taken from animals, the imme 
diately die; that blood is a sine qua non, is therefore evident. We see also 
by heterical induction that food taken into the stomach is not a sine qua non 
to the life of the foetus; nor is the respiration of atmosphere; but after birth 
both these things by homonical induction are sine quibus non. Now blood 
is compojed of fibrine and serum, and each of these has been analysed, and 
they are found to be isomeric, i. e., the constituents of the one and of the 
©ther are, not only similical differentia, but also by weight commensural in- 
commensura. It has been found also that if the blood be deprived of any 
one of its constituents, the health suffers; each one, therefore, by horntmical 
induction is a sine qua non. We can prove also by homonical induction that 
light is a sine qua uen of the growth and health of vegetables; for, other 
things being equal, they will not develope in dark cellars or caves. Most 

f plants contain organic acids in combination with bases such as potash, soda, 
lime or magr*esia; and hence it has been concluded, (but it is only probable 
and not an induction) that an alkaline base is a sihe qua non of growth of 
plants. The way to prove it is to make an experiment and have all other 
things, found in the soil and atmosphere where the plant grows well, present 
excepting these bases; if the plant will then not grow, we have made an ho- 
monical induction. 

In many of the sterile soils on the coast of South America, crops of 
grain will not grow at all; but if guano be put upon those soils, they then 
yield abundant crops; here is an hommiical induction respecting guano. 
And certain soils, which are entirely barren, may be rendered fertile by put- 
ting quick lime upon them. Soils also destitute of alkalies and phosphates 
will not grow certain plants, but if these be added, the plants then thrive 
upon them; here is an homonical induction. Homonical inductions respect- 
ing the necessary constituents of soils for raising plants may readily be made 
by comparing a productive with a barren soil. We take the following analy- 
ses from Dr. Leibig's agricultural chemestry. A, represents the surface soil; 
and B the subsoil. One hundred parts contain : 

A. B. 

Silica with coarse silicious sand 95,843. 95,180 

.Alumina 0.600. 1,600 

Protoxide and peroxide of iron 1,800. 2,200 

Peroxide of manganese a trace. 

Lime in combination with silica , 0,038. 0,455 

Magnesia in combination with silica '. . . . 0.006. 0.160 

Potasa and soda 0.005. 0.004 



# 16 

Phosphate of iron 0.198. 0.400 

Sulph uric acid 0.002. a trace 

Cloriue 0.006. 0.001 

Humus soluable in alkalies 1,000. 0.000 

Humus insoluable in alkalies 502. 0.000 

100,000. 100,000 

The above analysed soil was charactised by its great sterility. White 
clover could not be made to grow upon it; it, therefore furnishes one of the 
cases necessary for an homonical induction. In the following analysis 

we have: 

A. B. 

Silica and fine seliciou*. sand 94,724. 97,340 

Alumina 1,638 0.806 

Protoxide and peroxide of iron with maniranese 1,960. 1,201 

Lime T 1,028. 0.095 

Magnesia .' a trace. 0.095 

Potash and soda 0.077. 0.112 

Phosphoric acid 0.024. 0.015 

Gypsum. 0.010. a trace 

Clorine of the salt \ 207. a trace 

Humus •. 512. 0.135 

100,000. 100,000 

The above soil produced luxuriant crops of lucerne and sainfoin and 
all other plants whose roots penetrated deeply into the ground. Now T from 
these two cases, it would appear that in those plants receiving their norish- 
ment from the subsoil, humus was a sine qua non; while gypsum is indicated 
as a sine qua non in the surface soil. 

If we take muscular fibrine, which contains w T ater, and let it be ex- 
posed to a moist atmosphere, putrifaction takes place; but if the fibrine be 
dried and then exposed to a diy atmosphere, no such result takes place. 
Hence water or hydrogen, is a sine qua non of the putrifaction. So also 
yeast, whea completely dry, possesses no power to produce fermentation. 
Now yeast possesses a soluble and an insoluble substance, and the insoluble 
substance may be thrown out of the sine quibus non of fermentation by 
heterical induction; but the soluable part when exposed to the atmosphere 
produces fermentation, but when the atmosphere is excluded no §uch result 
takes place. An aqueous infusion of yeast may be mixed with a solution of 
sugar and preserved in hermetrically sealed vessels without undergoing the 
slightest chaage, but if exposed to the atmosphere fermentation immediately 
begins. Hence the soluble part of yeast and the atmosphere are proved to 
be sine quibus non of the fermentation which ensues in such cases. Several 
kinds of vegetable fibre, if kept secluded from oxygen or hydrogen, do not 
decay, but when oxygen and hydrogen are present decay commences; each of 



these, therefore, is a sine qua nop of such decay. Other bodies do not decay 
without the presence of a free alkali, and in such cases alkali by homonical 
induction is a sine qua non. The juice of grapes expressed under a receiver 
filled Willi mercury, which completely excluded the air, did not ferment; but 
When the smallest portion of air was admitted fermentation immediately be- 
gan. Animal food and vegetables may be kept for years without fermenta- 
tion, if the air be completely excluded. We have gone far enough to illus- 
trate the manner of making and the utility of homonical inductions. Any 
one of the cases of induction giyen above may be stated in the manner of 
formulae (3), in Chapter II. The only difficulty in arriving at conclusions, 
which may be confidently relied upon, lies in obtaining the precise data 
needed; if these can be had our conclusions are infallible. 

CHAPTER V. 

DIFFERENTIAL INDUCTION APPLIED. 

We have seen in' the previous book, that the homonical induction of 
aggregations only proves a certain aggregation to have been a sine qua non 
of a particular effect, but from this case we cannot, infer by ratiocination 
that this particular aggregation or a simile of it must be # a sime qua non of 
all similical effects. For, as there shown, two aggregations, as aggregations 
may be* differentia, and yet in the respect of the gregarium, which in one of 
the aggregations has been a cause of the given effect, the two may be inter se 
similia; and hence the necessity of differential and similical inductions. 
This matter lias been sufficiently^ explained heretofore. Now if we take a 
view of the elementary gases, we will see by differencial induction, that those 
gregaria, which distinguish gasses from liquids and salids, are not the causal 
gregaria of the peculiar action of any gass upon another substance; for, in 
these distinguishing gregaria gasses all agree. By differential induction we 
know, that the peculiar action of oxygen upon iron, for instance, is not owing 
to the distinguishing gregaria of a gass; for if it were, nitrogen would pro- 
duce upon iron a similical effect. The chemical action of liquids and of 
solids may be treated in a like manner. Each element possesses a chemical 
gregarium sui generis; and by differential induction we may frequently 
draw so near to this gregarium, which is a cause of certain effects, as to 
leave no doubt of the causal gregarium, though differential induction does iv t 
directly determine causes. Complete differential inductions of all the ele- 
ments would lay the foundations upon which chemestry might be made a 
deductive science; whi oh may, as we hope, tn accomplished in the future. 
'But for the illustration of our present subject, we must proceed with such 
data as experimentalists have furnished. And we may commence, not with 
the differential induction of elements, but of compounds. One element may 
not exert some peculiar force without the presence of another or others, with 



18 
which it is compounded, and then this peculiar coinpound'is the sine qua 
non of a given effect. This is owing to the circumstance, that compounds 
possess capacial gregaria, which, with reference to the gregaria of either of 
the elements entering into them, are differentia. We may begin our illustra- 
tions, therefore, by differentiating compounds. And as by analysing com- 
posite substances, they are resolved into simple differential compounds, we 
may assume, for the sake of illustration, that each of the simpler compounds, 
into which a composite substance can be resolved, exerts its gregaria unim- 
peded when in the more complex substance. 

Now according to Braudes, rhubarb contains: Rhubarbic acid; Galic 
acid; Tannin; Sugar; Colouring extractive; Starch; Gummy extractive; 
Pectic acid; Malate of lime; Gallate of lime; Oxalate of lime; Sulphate of 
pottassa; Cloride of pottasium ; Silica; Phosphate of lime; Oxide of iron ; 
Lignin; Water.' And if by differential induction we are in search of the 
purgative ingredient of rhubarb, we may differentiate water by a comparison 
of rhubarb with the juice of the sugar cane, both contain water, they agree 
in this respect; we may differentiate lignin by a comparison with almost any 
woody fibre; the oxide of iron and siiica by a comparison with the water 
from wells and thermal springs; phosphate of lime by a comparison with 
bone dust cloride of pottassium by & comparison with sea-water; the sul- 
phate of pottassa by a comparison with potashes; the oxalate of lime by a 
comparison with w r ood-sorrel ; Gallate of lime by a comparison with gall- 
nuts; the malate of lime by comparison with vegetables such as the house- 
leek ; Tannin by a comparison with the bark of oaks; sugar and starch by 
comparisons with wheat flour and maple saps &c. As the above compounds 
can be separated, we could use heterical and homonical inductions, and that 
is the better way, for, it relieves us from making an assumption at the outset 
which may not be true; but tor the sake of illustration w T e have used differ- 
ential induction. If we wish to find by differential induction in what the 
poisonous gregaria of morphia consist, we may analyze this compound and 
we find it to contain carbon, hydrogen, oxygen and azote. We can differ 
entiate the carbon by the comparison with fat beef or pork; the hydrogen 
and oxygen by a comparison with water ; and the azote by a comparison with 
glliten or indigo. And hence it appears that neither of these elements per se 
is the cause of the poisonous effects of morphia, but that the causal gregaria 
arise from the compound. There is in this induction, however, the same as- 
sumption, which we made, when, treating of rhubarb, and though, we think, 
we are at liberty to make such assumption for the sake of conveying to the 
reader's mind the application of a principle yet in the actual search after 
truth, such assumption is inadmissable. We must deal with morphia, there- 
fore, not by its ingredients, but b\^ its gregaria. 

Now morphia among others coontains the following gregaria. 



.19 

Morphia. — It is fusible at moderate heat; it burns with a red and very 
smoky flame; it is soluble fn 30 parts of boiling anhydrous alcohol; it is 
soluble m 500 parts of boiling water; it is insoluble in cold water; it is in - 
soluble in ether; it is insoluble in oil; it is insoluble in chloroform ; it forms 
salts with acids. 

We will assume that the above data are correct, though chemists differ 
respecting some of the gregaria. Tne Following are some of the gregaria of 
starch a non-poisonous substance: 

Starch- It is insoluble in cold water; it is insoluble in cold alco- 
hol; it is insoluble in ether; it is insoluble in oil. 

The following are some of the gregaria of resin a non-poisonous 
substance. 

Resin. — It is fusible at moderate heat; it is insoluble in water; it is 
translucent; it burns with bright flame and very much smoke. 

Now, if we compare morphia with these last two non-poisonous sub- 
stances we will see that several of their gregaria are inter se similla; these 
gregaria, therefore, may be differentiated from the poisonous gregaria con- 
tained in morphia, and further investigation must be had. 

Again; we know that common salt, cloride of sodium, is an antiseptic 
and when applied to fresh flesh it prevents decay; we may inquire therefore, 
respecting the causal gregarium of this phenomenon. Now among the gre- 
garia of common salt are the following: 

Salt. — ;It has a white color; it has a saline taste; it undergoes but 
little change in a dry atmosphere; it dissolves in water; it dissolves but little 
in alcohol; it melts by heat; it is decomposed by carbonate of potabsa.' 

With common salt we may compare Epsom salts, sulphate of mag- 
nesia, which among others contains the following gregaria: 

Epsom Salts. — It has a white color, it has a saline taste, it undergoes 
but little change in a dry atmosphere, it dissolves in water, it dissolves but 
little in alcohol, it nielts by heat, it is decomposed by carbonate of potassa. 

Now the similia may be differentiated from the causal gregaria and 

the matter must then be further inquired into. We have gone far enough 

with our illustrations to see that true differential inductions can be obtained 

only from the comparison of gregaria. And any one who will examine the 

matter, will find, that in what Bacon would call the history of substances, 

chemical science is yet very defective. We need further experiments to f be 

made under the guidance of a true philosophy. 

CHAPTER VI. 

SIMILICAL induction applied. 

As heterical induction clears the way for homonical induction, so 

differential induction prepares the way for similical induction. And both 

differential and similical inductions to be satisfactory must be based upon a 

great number of gregaria, which requires a very extensive knowledge of 






20 

substances. We do not propose to give complete and wholly satisfactory in- 
ductions respecting the causal gregaria of effects;' for that would require a 
different kind of treatise from the one upon which we are now engaged, but 
we merely propose to illustrate the principles of induction and let scientific 
men, each (me in his own special department, make the application with full 
data to particular subjects. Now if we wish to find the poisonous gregarium 
or gregaria contained in Muriatic or Sulphuric acid, we may examine their 
gregaria in the following manner. Some of the gregaria of Muriatic acid 
are as follows: 

Muriatic Acid. — It is a colorless liquid, it has a sour taste, it corrodes 
animal tissues, it is incompatable with metal ic oxides, it is incompatabie with 
alkalies, it redens litmus paper, it has a strong affinity for water. 

The following are some of the gregaria ot Sulphuric acid: 

Sulphuric Acid.— It is a colorless liquid, it has a sour taste, it cor- 
rodes animal tissues, it is incompatable with metalic oxides, it is incompata- 
ble with alkalies, it redens litmus paper, it has a slrong affinit}^ for water. 

For the purpose of differential induction we may compare with the 
above acids the acetic acid of commerce, a substance which may be tajten in 
large quantities without poisonous effects. Some of the gregaria of acetic 
acid are as follows: 

Acetic Acid.— It is a colorless liquid, it has a sour taste, it is incom- 
patable with metalic oxides, it is incompatable with alkalies, it redens litmus 
paper, it has a strong affinity for water. 

Now if we differentiate the similical gregaria of acetic acid from the 
poisonous gregaria contained in sulphuric and muriatic acids, we find the 
latter two acids to agree in their gregaria of corroding animal tissues. And 
by similical induction this corroding gregarium is a causal gregarium of the 
poisonous effects; it produces the direct, destruction of the organs with which 
it comes in contact, and hence death ensues. 

There is another class of poisons, which do not corrode or immedi- 
ately destroy the-organs with which they come in contact, but by their action 
they, render the tissues incapable of performing their functions. Of these we 
ma3 T compare the salts of lead and of copper. 

The following are some of the gregaria of the carbonate of lead: 

Carbonate of Lead. — It is a white solid, it is insoluble in water, 
it is soluble in acid, it is soluble in alkali, it enters into firm combination 
with animal tissues. 

The following are some of the gregaria of what is commonly called 

verdegris, the carbonate of copper: 

Carbonate of Copper.— It is a green solid, it is insoluable in water, 
it is soluble in acid; it is soluble in alkali, it enters into firm combination 
with animal tissues. 

For purposes of differential induction we may compare pure indigo 

with tli-e above: 



21 

Indigo.— It is a blue solid, it is insoluble in water, it is soluble in 
acid, it is soluble in alkalif 

After differentiating we find carbonate of lead and copper to agree in 
the gregarinm of entering into firm combination with animal tissues; and 
vital organs thus rendered calous and inflexible can not, of course, perform 
their functions, and hence death must ensue. We do not, however, give the 
above as satisfactory inductions; the data are insufficient and some of them 
may not be correct. Chemists have not been familiar with the inductive pro- 
cesses and they have not looked for data in view of making differential and 
similical inductions, and hence they have not furnished us with the requisite 
ground- works. 

As another case to illustrate the principle of similical induction we 

may inquire into the causes of the double refraction of light. . Borne of the 

gregaria of the carbonate of lead, which substance causes double refraction, 

are the following: 

Carbonate of Lead. —It is a transparent substance, it is of crystaline 
structure, its crystals are of the rhombohedral form, it is insoluble in water, 
it is soluble in acid, it is soluble in alkali. 

The following are some of the gregaria of Iceland spar, another sub- 
stance causing double refraction : 

Iceland Spar.— It is a transparent substance, it is of crystaline struc- 
ture, its crystals are of -the rhombohedral form, it is insoluble in water, it is 
soluble in acid 

The following are some of the gregaria of one species of diamond, 

which causes double refraction: 

Diamond. — It is a transparent substance, it is of crystaline structure, 
its crystals are of the rhombohedral from, it is insoluble in water, it is soluble 
in acid. 

With the foregoing double refracting substances we may compare the 
following substances, which do not refract light in that manner. The follow- 
ing are some of the gregaria of a species of diamond which causes single 
refraction : 

Diamond. — It is a transparent substance, it is of crystaline structure, 
its crystals are of the octohedral form, it is insoluble in water, it is soluble 
in acid. 

The following are some of the gregaria of pure rock salt: * 

Rock Salt. — It is a transparent substance, it is of crystaline structure, 
its crystals are either of the cubical or octohedral form but sometimes pris- 
matic, it is insoluble in water, it is soluble in acid. 

The following are some of the gregaria of pure borax: 

Borax. — It is a transparent substance, it is of a crystaline structure, 
its crystals are either of the prismatic or octohedral form. 

Now after using differential inductions we find the substances causing 
double refraction to agree in having their structure made up of rhombohedral 



22 

crystals. And from this it would appear that the form of the crystal causey 
double refraction; but our data are again in'sufficiest for a satisfactory induc- 
tion. There are fourteen different forms of crystals entering into the struc- 
ture of diamonds and only two of which, the octoheclra and cube, so far as 
we can learn, cause single refraction. The subject needs further examina- 
tion with more full and more certainly correct data. Fesnel explains, deduc- 
tively, double refraction by assuming that the ether in double refracting sub- 
stances is not equally elastic in all directions. This is, of course, merely an 
hypothesis, and the evidence by which it can be inductively proven is not 
furnished by double refracting substances. Newton concluded, probably 
per enumerationem simplicem, that combustibility was in some way a cause 
of refraction and then reasoning a posteriori he conjectured that water and 
the diamond would be found to contain combustible elements; and his con- 
jecture has been verified. But we have gone far enough to illustrate the 
principle of similical induction. 

CHAPTER VIL 

INCOMMENSURAL INDUCTION APPLIED. 

We have seen, heretofore, that there are three cases of incommensural 
induction, having reference to three kinds of relations between the causes 
and their effects. And if we commence our illustrations with incommen- 
sural 'quantities of certain objects, which we are examining for the purpose 
of determining their relations to certain incommensural effects, we will soon 
see the utility of this method from the daily necessities of life. On making 
our fires in the stove, we need but. admit a small current of air and then a 
greater one to convince us, by incommensural induction, that the atmosphere 
is connected, in some manner through causation, with the combustion going 
on in the stove. And we need but increase the inhalation of oxygen into our 
lungs to find out, that certain phenomenal effects in our system are clepedent 
upon the respiratiou of this gass. The incommensural quantities of the 
sun's rays falling vertically and obliquely upon equal areas in different lati- 
tudes, must also convince us of their relations through causation with the 
earth's temberature and vegetation. And in every branch of agriculture, 
horticulture and floral training, the case of incommensural inductions from 
the relations of quantity may be made by a little ingenuity. I extract the 
following facts from Prof. Liebig's agricultural chemistry: "The employ- 
ment of animal manure in the cultivation of grain and the vegetables which 
serve for fodder to cattle, is the most convincing proof that the nitrogen of 
vegetables is derived from ammonia. The quantity of gluten in wheat, rye 
and barley, is very different; these kinds of grain also, even when ripe, con- 
tain this compound of nitrogen in very different proportions. Proust found 
French wheat to contain 12.5 per cent, of gluten; Vogel found that the 



23 

Barvanan contained 24. per cent; Davy obtained 19.' per cent, from winter 
and 24. from summer wheat; from Sicilian 21. and from Barbary wheat 19. 
per cent. The meal of Alsace wheat contains, according to Boussingault 
17.3 per cent, of gluten; that of wheat grown in the 'Jardin des Plantes' 26.7 
and that of winter wheat 3.33 per cent. Such great differences must be ow 
ing to some cause, and this we find in the different methods of cultivation. 
An increase of animal manure gives rise not only to an increase in the num- 
ber of seeds, but also to a most remarkable difference in the proportion of 
the substances containing nitrogen, such as the gluten which they contain. 
* * * * * One hundred parts of wheat grown on a soil manured with 
cow-dung (a manure containing the smallest quantity of nitrogen) afforded 
only 11.95 parts of gluten and 64.34 parts of amylin or starch; while, the 
same quantity grown on a soil manured with human urine, yielded the max- 
imum of gluten, namely 35.1 per cent. Putrified urine contains nitrogen in 
the forms of carbonate, phosphate and lactate of ammonia and in no other 
form than that of ammonical salts." Now, in the above facts, granting the 
soils and atmospheres to have been in all other respects inter se similical and 
commensural, there is a fair incommensural induction respecting ammonia. 
In another case of incommensural induction, we have seen that, ceteris 
paribus, the spaces between an object containing causal gregaria and the incom- 
mensural effects are incommensural ; and we w r ill now proceed to give a few 
simple illustrations of this case. It is said that Galileo, perceiving that the 
chandeliers suspended in a church, when set in motion, vibrated long and 
with uniformity, was led by these phenomena to invent the pendulum. With 
this instrument a great many persons have since experimented; and the phe- 
nomena of its vibrations are found to be incommensura in different latitudes 
and localities. A pendulum of about 39 inches, which vibrates seconds in 
the latitude of New York, will not vibrate sixty times in an hour of com- 
mensural time on the equator; and there is a marked difference in the time 
of the vibrations of the same pendulum in the valleys of the Amazon and on 
the high peaks ©f the Andes. The farther you remove the pendulum from 
the earth's center of gravity, the fewer will be its vibrations, ceteris paribus. 
And hence we learn from these incommensural relations of spaces between 
the earth and the incommensural effects, that the earth contains causal gre- 
garia of these phenomena. Again : The surveyor,from the incommensural rela- 
tions of spaces between his compass and a certain hill and incommensural 
variations of the needle from the true meridian, concludes that the hill pos- 
sesses causal gregaria of these variations. The incommensural relations of 
the spaces, between the moon and the waters on different parts of our earth, 
and the tides, furnish also the data from wiiich to make incommensural in- 
ductions; and although the tides, on the opposite side of the earth from the 
moon, might seem at first thought, to destroy the force of these data, yet when 



24 

we reflect that the earth is interposed between the moon and those tides, the 
data remain in their validity. The reader will understand that in incom- 
mensural induction from incommensural relations of space, we are seeking 
merely for some object which contains causal gre^aria of the incommensural 
effects; no matter what may be the characters, in other respects, of the in- 
commensural effects in their relations inter se. Thus: if we try the posi- 
tively electrified end of a cylinder with the knob of a charged Leyden jar 
and find the cylinder to be repelled, and then we try the negative pole of the 
cylinder and find phenomena of an opposite character, by incommensural 
relations of space and the incommensural effects of each kind inter se, i. e. f 
incommensural similia both these sets of phenomena, though inter se differ- 
entia, are proved to have a dependence upon the knob of the jar, i. e., the 
kn©b contains causal gregaria of both these sets of phenomena. 

We will now give a few illuitrations of the case in which incommen- 
sural inductions can be obtained from incommensural relations of times. If 
we should find find by tne side of a mountain a ledge of iron ore which had 
been uncovered for but a quarter of a century, and on the same mountain we 
should find ore, which had been bare for several centuries, and we should 
make comparisons between the two, we would be able to draw, from the in- 
commensural effects perceived in the ores, conclusive incommensural induc- 
tions of the cause from the incommensural relations of times, had we never 
thought of the cause before. For,- granting that all other things are similical 
and commensural in the two sets of phenomena excepting the times of ex- 
posure to the atmosphere, and the quantities of atmosphere being commen- 
sura in commensural times, no object whatever, excepting the atmosphere 
could have incommensurated the effects witnessed in the oxydized ores. A 
hound by instinct as we call it, makes a kind of inverse incommensural in- 
duction concerning incommensural effects from incommensural relations of 
time, or we, at least, may make it for him, when he is pursuing the trail of a 
deer. Each tread of the deer deposits in the soil a certain effect, and these 
effects immediately after the treads in similical soils are, no doubt, very nearly 
commensural inter se, and which the atmosphere with the soil comences to 
diminish, leaving at incommensural intervals of time from the point from 
which they were made incommensural effects. When the houn^, therefore, 
strikes a rather old track, not having a scientific knowledge of the relations of 
time, space and velocity, and no means, in the present case, of judging of the 
last, he is not very animated in the pursuit, not expecting to find the deer for 
some time, although it may have lain down within forty rods from the point 
where he struck the trail. But as he moves on, he perceives incommensura; 
he then increases his speed, and finding the degrees of the incommensura, or 
differences, to increase rapidly, he becomes warm and boisterous, proclaim- 
ing as he goes the state of his expectations, in relation to time of coming up 



25 
■with the cause of these incommensural phenomena. Should a man buy two 
pair of boots Inter se similia, and walk in one pair over a given road for 
six hours a day for two months, and then in like place and manner walk in 
the second pair for four months, and observe the incommensural effects and 
times, he would not hesitate to make an incommensural induction. We need 
go no further with illustrations. 

It must have been noticed by the reader that when we are considering 
incommensural effects inter se, our comparisons have reference to nothing 
else than quantity, i. e., the effects inter se are quantitively ineommensura. 
It will be noticed too, that drops of water inter se commensural falling at in- 
tervals of one second for one year, and commensural drops falling in like 
manner for half a year, produce incommensural effects from the incommen- 
sural quantities of cause. And when an aggregation exerts from itself in- 
fluences through space, as in the radiation of heat for instance, an object 
nearer and one more remote from the focus of influence, prodding the objects 
he inter se commensura, will receive incommensural qaantities of the 
influence in commensural times. And hence, laying aside the interference of 
causes, the quantities of causes and effects are proportional. The assertion 
that effects are proportional to their causes, however, must not be understood 
to mean that such is the case absolutely and without limit, as we will better 
understand hereafter. 

CHAPTER VIII. 

COMMENSURAL INDUCTION APPLIED. 

Commensural like incommensural induction deals only with effects, 
which are inter se similia. And we take a certain case, in which we have 
heretofore determined a certain object to contain causal gregaria of a specific 
effect, and having determined the time space and quantity in this case, we 
endeavor to ascertain what objects, over which we may have no control, con 
tain similical gregaria with reference to such similical effects, from the rela- 
tions of the time, space and quantity of the case in which the object is under 
our control to the time, space and quantity in other cases of similical effects 
in which the objects containing causal gregaria are not under our control. 
And in commensural as in incommensural induction there are three cases. 
Let us commence our simple illustrations with the commensural relations of 
space. Suppose, for instance, we had made experiments with a certain ivory 
ball and found that when w T e let this ball fall forty feet upon iron of a smooth 
surface, it rebounded a certain number of feet; when we let it fall upon 
marble in like manner it rebounded a certain other number; and when upon 
brass in like manner a certain other and so on: and in all these experiments 
we will suppose the plates of the different metals and minerals with which 
we experimented to be quite thick and placed upon solid granite rock. The 



20 

rebounding of the ball is the effect in the ball witnessed by us, of which the 
space through which it rebounds is the quantum: and some of the causal 
gregaria of this effect are in the ball and the others are in the objects up^n 
which it fell. Suppose- now, after this, we rind a mass of metal, of a kind 
unknown to us, underlain with granite and we let the same ivory ball fall 
upon its smooth surface forty feet and observe its rebounding, and we find 
this effect to be commensural with that obtained when it was let fall upon 
marble; then as the ball is the same and other things are equal, theeommen- 
sural relations of the spaces fallen through by the ball in the two eases to 
the commensural effects, convince us by commensural induction, that this 
new metal contains, in the respect to these similical and commensural effects 
similical and commensural causal gregaria with those contained in marble. 
And should this new metal be so situated that, we could not approach to it so 
as to examine it closely with our eyes or feel it with our hands and the ball 
used be an heterical one, but similical and commensural with the first, the 
result would be the same. Again: Suppose we make experiments with a 
certain magnet and find that if we attach the one end of a small string to the 
north pole of a magnetic needle placed at a certain distance from the magnet 
and the other end to a weight, which the magnet, when the magnetic needle 
is at right angles to it, will just be able to draw on a certain surface until the 
needle points directly towards the magnet, this drawing of the weight then 
may be taken as the quantum of the effect: it we now take a piece of ©re 
and situate the needle with weight attached on the same surface as before, 
and a commensural effect be produced, we conclude by commensural induc- 
tion, having our eye on the commensural relations of the spaces in the two 
cases and times being supposed commensural, that the magnet and ore con- 
tain similical and commensural causal gregaria. Again; if we make a fire 
in a stove and hold a thermometer at a certain distance from it and read the 
degrees to which the mercury rises in a given time, this rising of the mer- 
cury will be the quantum of the effects; if then we go to a heap of quick 
lime with water thrown upon it and covered up with earth, and we place the 
^thermometer at a commensural distance from it and find the quanta of effects 
to be inter se commensural, we conclude that the heap contains similical and 
commensural gregaria, respecting such effects, with the stove. * 

Second Case. — If we take the down of the goose and find that a certain 
quantity will be attracted through a certain space in a given time by the 
prime conductor of an electrical machine, and we then take a commensural 
quantity of the down of the swan and find it to be attracted through the same 
space in a commensural time, we conclude the latter substance to contain 
similical and commensural causal gregaria with the former. If a weight be 
attached to a baloon and the baloon then ascend a given distance in a certain 
time, and we then attach the same weight to another commensural baloon 



£7 

and the second one make the same distance in a commensural time, the two 
baloons contain similical and commensnra gregaria; 

Third Case. — If we charge a certain Leyden Jar to its capacity and 
measure the space through which a spark from the knob can be made to 
pass so as to ignite sulphuric ether and then we discharge a spark of the jar 
commensurally charged through the same space into ether of alcohol and 
find commensural effects, times being equal, we conclude the tw T o ethers to 
contain similical and commensural causal gregaria with reference to such 
effects. We need wot illustrate farther. If the reader will bear in mind that 
all effects are produced by heterical causal gregaria, some of which are in 
the objects in which we witness the effect, and some in another object, 
numerous examples, from which commensural inductions can be made, will 
suggest themselves to his own mind. And it is evident that if we can not 
always find commensural relations, we may yet make our inductions in many 
cases by the commensural relations of mathematical ratios. By taking a 
piece of iron, for instance, to incommensural distances from the earth's sur- 
face and finding the ratios of its weights and distances, we find that gravity- 
varies inversely as the square of the distance; we find also that the matter 
tends to move in straight lines with a force equal to its weight multiplied 
into its velocity; and therefore, near the surface of the earth if we project a 
stone of a certain weight in a horizontal direction with a given velocity, w r e 
can calculate the distance it will make through space in falling to the earth 
by gravity. Now if w'e contemplate the moon and find its ratios to be com- 
mensural with the ratios of our experiment with the stone, we conclude by 
commmensural induction, that the moon and the stone contain similical 
causal gregaria. In this manner Newton extended gravity to the moon, and 
it has since been extended to other heavenly bodies; and it is. supposed, by 
inductio per enumerationem simplicem, to exist throughout the universe. e 

CHAPTER IX. 

THE DENOMINATE UNIT. 

Those who have masUred the principles of books I and II, and of the pre- 
vious chapters in this book, (which in the last four chapters we have endeav- 
ored to render more easy for the understanding by giving simple illustrations 
with sensuous objects) will be able now to proceed further with us in our 
still deeper inquiries into nature's processes. In our previous inquiries, ex • 
cept in similical and differential inductions, we have dealt mostly with ag- 
gregations, and have not given much of our attention to gregaria, from which 
only, those relations, which are called the laws of nature, can be evolved. 
And we have seen, heretofore, that homon per se makes no part of our knowl- 
edge, but that we gain our knowledge of homon by means of hetera; but our 
knowledge of similia and of differentia is not predicated upon hetera alone, 



23 



but upon siimlical and differential relations of gregaria; and if we can deal 
with these gregaria so as to discover the laws of causation by which they act, 
we will have to enter nature's mysteries in this regard by getting hold of re- 
lations existing inter gregaria. Now, nature is more accessible in some 
points than others, and her relations of quantities are most easily compre- 
hended by us; we will, therefore commence to evolve the laws of gregaria 
by investigating their quantitive relations. But for this purpose we need 
denominate numbers, which have an homonical standard of measure; and 
space is the only thing from whicji we can gain such denominate and 
homonical unit. We will, therefore, treat briefly of the denominate unit in 
this chapter. 

If the hand of a clock, when it ticks once, posses from a to b (Fig. 1.) 
in the small circle of the diagram, while a body 
on the larger circle passes from c to d, we may 
take the well known equation in natural 
philosophy S 

/ in which relations the space from a to b may be 

made the denominate and homonical unit of 

measure; and if this unit will apply twice to the 

space from c to d then 2 

V= — = 2. 

1 

The space from a to b may be made also the homonical unit of measure for a 
steelyard, a barometer, a thermometer, steamguage, momentum, dry measure, 
liquid measure, money and throughout nature. . 

Then let V stand for velocity, S for space, T for ttme, W for weight, and 
M for momentum, and take the following equations in natural philosophy: 

G. 
M 



QQ 




3. 



o. 



1. 2, | 

S S M 

V = _ S = YT T = — W= — M = VW V = — 

T V V W 

Now if Y in equations 1, 2 and S be equal to V in equations 4, 5 and 6 
as it may be, and we take the value of V as given in equation 6 and put it 
for V in equations. 1, 2 and 3; and we take the value of V as given in equa- 
tion 1 and put it for Y in equations 4, 5 and 6, we will have the following 
equations: 

7. 8. 9. 10. 11. 12. 

S MT SW MT SW S M 

- — S = T bt W = M is — = — 

W M S T T W 



M 
W 



29 

Gravity, in a body above the earth's surface, is nothing else than the 
tendency of the aggregation to fall to the earth, and the quantum of space 
occupied by incommensural aggregations inter se similical, which is found 
by multiplying together their lengths, breadths and thickness, is in propor- 
tion to the quantum to this tendency to fall. If we take two pieces of lead 
inter se similical, but occupying incommensural spaces, the piece occupying 
the greater quantum of space at commensural distances from the earth's 
center of gravit}^ will possess a greater quantity of gravity than the other. 
Now by experiments it has been ascertained, that gravity above the earth's 
surface, varies inversely as the square of the distance from the earth's center, 
or directly as the ratios obtained by dividing the square of the radius by the 
square of the distance from the earth's center to the body above the earth's 
surface. And hence let G stand for gravity, r for radius, Q for quantity of 
matter, and S for the distance of the body from the earth's center, and we will 
have the following equations: 

13. 14. 15. 

Qr3 S2G Qr2 

G = Q = S2= — 

S3 r2 G 

Now if S in equations 1, 2 and 3, be equal to S in equations 13, 14 and 
15, as it may be, and we substitute the value of S as given in equation 2. for 8 
in equations 13, 14 and 15, and the value of S as given in equation 15 into 
equations 1. 2 and 3 we will have : 



16. 


17. 


18. 


Qr* 


V2T2G 
Q = 


Qr2 

V2T2 — 




G 

V2T2 r2 

19. 20. 21. 

Now what is called the specific gravity of bodies, i. e., the relation of 
gravities between a certain quantity of water or air, and a commensural 
quantity of differential substances as measured by space, varies directly as 
the ratio obtained by dividing the gravity of a certain substance by the 
gravity of a commensural quantity of water or air. Hence let Q stand for 
the commensural quantity of any substance, 1 for the gravity of a quantity 
of water equal to Q, and G for the gravity of Q in any other substance than 
water and S for specific gravity, and we will have the following equation : 



80 

G 

22. S = — 

1 
And if G in equation 22 equal G in equation Hi, and we substitute we 
will have: Qr^l 
23. S = . 

And in all the foregoing equations the standard of measure is a denominate 
and homoniCal unit of space. 

CHAPTER X. 

iiATro. 

If one of two numbers be made the numerator and the other denomi- 
nator of a common fraction, the ratio of the numerator lo the denominator 
is such number, that if von multiply the denominator by it you will ha vet he 
numerator, and if you divide the numerator by it you will nave the denomi- 
nator: and the ratio of the denominator Jo the numerator is such number, 
that if you multiply the numerator by it you will have the denominator, and 
if yon divide the denominator by it you will have the numerator; and as the 
ratio of two numbers generaHy appears in the form of a fraction, (which 
however, may sometimes be a whole number) when you have the ratio of the 
numerator to the denominator, if you invert- the terms of the fraction, you 
will have the ratio of the denominator to the numerator, and vice versa: 
Now all persons, who have studied mathematics, will understand the follow- 
ing propositions : 

() a qc a 

rtX0=0. — -0, -i-==cb. — — 0. — =1. —=ao. — =0. *X0=1. and — =1. 

a a - °° « 

In these propositions zero or 0, is to be understood as meaning an infinitesi- 
mal quantity, i. e., a quantity dess than an? assignable quantity and x is its 
reciprocal. 

Now none of the foregoing propositions, excepting the last one, heed 
any explanation for the mathematicians; the symbol 


however, needs some explanation as life mathematical treatises used in our 
schools and colleges have not given to it its true significance, which we will 
now proceed to explain. Take the proposition 

1. x= • , 

a*— b2 

If in this equation we make a— b, we will have 





But in equation 1 the numerator is a multiple of a — b, and it may be 
put inm the form of (a— b) (a^+ab-f-b2) ; and the denominator is also a 
multiple of (a — b), and it may be put into the form of (a — b) (a-f-b), and then 
we will have 



31 

(a-b) (a2+ab+b2) 

3. x== X . 

(a— b) (a+b) 
Now from this equation we may have 

(a2+ab+b2) OXaH-OXab-fftXbs 

4. x=— X — — — ~ =---1 : 

(a+b) (OXa+Oxb) 

Or we mav have 

(a2-fab+b2) ( a 2+ab+b<g) 3a2 3a 

(a+b) (a+b) 2a 2* 

How are those incomraensural results to be explained ? Mow as 




1 is the ratio of the numerator to the denominator and also of the denomi- 
nator to the numerator, as it always is when the numerator and denominator 
are absolutely commensura; thus 4 8 

— =1, — =1, — — 1, etc. 
4 8 

And it is evident that in equation 4 we have taken the fraction 

a2+ab+l)2 



a+b 
and multiplied its numerator and denominator by the common intinitesmai 
quantity a 

GO 

while in equation 5 we have multiplied the same fraction by the ratio of 

a a 
—-.to—' 

QO GO 

i. e., by the ratio of commensural quantities. Now it is evident that when 
the numerator and denominator of a fraction are commensura, their ratio 
will be the denominate unit, and it is also evident that, in all proper fractions 
the ratio of the numerator to the denominator will be less than the denomi- 
nate, unit: it is also evident that the difference between J£ and J£ will be a 
greater quantity with reference to the denominate unit, than the difference 
between % and 3^> while their ratios are commensura: thus %- :- %=% and 
M^M^Mand %=%; but %-%=}£ and J^-% = % and }£>%. "And the 
greater the decrease of the numerator and denominator, while their ratios 
remain commensura, the less will be their difference in numerical value com- 
pared with the denominate unit; and hence the difference between the 
numerator and denominator may become infinitesmal and the ratio all the 
time remain the same, i. e., 0— 0<0, while 0-^0—1, results, which can only be 
true of infinitesmal quantities in their relations to our minds. And if by 
we mean absolutely nothing at all, 0—0 is nothing, 0—0 is nothing and 6x0 
is nothing; and if by go we mean something without limit, cox co is not 
within our conceptions, nor is co-f- go. But although we can not conceive of 
absolute existences, and of course can not deal with them intelligently, yet 
we can conceive of finite relations as being absolutely commensural and in- 
commensural and hence if we have equation 4 or 5 as above, we- may con- 



32 

ceive of the relations of a— b in the numerator and in the denominator as 
absolutely eommensural, and of a and b as absolutely com men sura, and then 
the relations contained in a— b 

a— b 
will destroy each other and this fraction will have no relation to offer towards 
the other factor, i. e., its relations will be a nonentity and it need not be con- 
sidered, but if a — b in the denominator be an inflnitesmal quanity and a— b 
in the numerator be an absolutely eommensural infinitesmal quantity, 

a-b 

a-b 
will absolutely equal 1, the denominate unit; and we have seen in the pre- 
vious chapter, that the denominate unit is the space which is the homonical 
standard for tbe measurement of time. Now whenever any number is mul- 
tiplied by 1 the number is taken one time, i. e., its value is not affected; and 
whenever a number is multiplied by absolutely nothing, i. e., not touched at 
all, its value is not affected'; and hence any number multiplied by absolutely 
nothing- will remain in the same relations, as when it is multiplied by the 
ratio of two numbers, whose difference is absolutely nothing; and therefore 
in equation 4 we multiplied both numerator and denominator b} T an inflni- 
tesmal quantity, which produced products whose difference was not abso- 
lutely nothing though taken'te be so, while in equation 5 we multiplied b} r 
the ratio »f two numbers, whose difference was absolutelynothiug, and hence 
the incommensural results. And vrpon the supposition with which we started, 
i. e., that a was absolutely equal to b, equation 5 contains the true result. 

Now from the the foregoing discussion it will appear that, the symbol 
/- may be made to make its appearance in every ratio by factoring and sup- 
posing the difference between the numerator and denominator of one of 
the factors ;o be less than any assignable quantity: thus the ra-tio of 4 
is 72, which may be equal to a — 

b 
when the difference between a and b is less than any assignable quantity and 
we multiply by their ratio; but if we multiply by the quantities themselves 
we will have 

4 

i. e., we will have 1 instead of H- To illustrate by figures let }^~ — x% 

and if 4~ 4 absolutely and we multiply by their ratio we will have }4~lX% 
— %, or *f we multiple in, we will have 4x1 4 

%= =-—=% 

4X2 8 
but if 4 and 4 be reduced to infinitesimally small quantities and we multiply 
in we will have 

or if 4 and 4 be made enormously large quantities 

we will have ^ 

M= — 1. 

00 And hence the svmbol — 









is the ratio of infini- 
tesma'te, anil ff 

o^ is its reciprocal ; and the ratio of these ratios is 1 ; Urns 

6 '°° °° 

i. e., the ratio of ratios, which are reciprocal, is always the denominate unit; 
and hence the true significance of qo 

— and — 

CTj is ratio of reciprocal ratios. 

If we lake the equation a-— b- 

0. x=^= 

(a— b)2 and make a— b infinitesimally we 

will have 7. X— : — ===1; 

but by factoring and cancelling we will have 

a-j-b a-b a-f-b 2a 

a— b a— b a— b 
Now if bv we mean absolutely nothing then x— 2a, and 
x 2a 2a ' 

— =- . i.o., — will be the true ratio of x to 1; and if by we mean an in • 

11 1 . X a, qo 

finitesmal quantity then x==co and —= — , i. e., — will be the true ratio of x 

11. 1 
to 1; but the two values of x are in com men sura, i. e., in the first case it is 
finite and in the second it is infinite: and we will have the proposition 
9. x : l::oc;l, xXl-=cc-}-l— = op. Again take the equation 
(a-b)3 

. 10. x—- and by making a=b infinitesimally we will 

a3-b ; 3 * 1 3a£ 

have 11. x— • — , this last equation mav be stated thus — = — 

3a2 x 

1 &*2 3a 

and if by we mean absolutely nothing we will have — === — , i. e., — will be 

x .1 1 

Ihe true ratio of 1 to x, and if bv we mean an infinitesma] then x=0 and 

1 1 
we will have — ==— ; but the two values of x are incommensura., i.e., in the 

x 
first case it is finite and in tne second it is infinitesma! : and we will have 

the proportion X-1--0 1, xxl=0xl=0. ' And from the above we see 

1 oo 1 

that — , or — , or — , or — , may be a ratio and may have a ratio. And we 

1 1 ' ; '■■ Q0 

oc oo o, 

mav have — === — , and'— =-- ; and hence — or — may be a ratio and may 

OD GO CO • 

have a ratio, and they and their ratios are the reciprocals of each other. 

Now the whole object of differential calculus is to determine the ratio 
of rates, i. e., to determine the ratio of ratios; for rate and ratio, when applied 
to motion or increase, are the same thins:. And the ratio of one constant 



34 

number to another is easily found by the ordinary principles of Arithmetic; 
it is easy also to find the ratio of rates of the movements of two bodies, when 
their rates are uniform, i. e., when each one for itself makes commensural 
spaces in com mensural times; but when the rate of one is uniform and the 
rate of the other proceeds upon some law other than that of uniformity, i. e. 
when it does not make com mensural spaces in commensural times, a case is 
presented for the differential calculus. Let us then examine the following 
Theorem in the calculus: "The rate of variation of the side of a square is 
to that of its area, in the ratio of unity to twice the side ot the square. " 
This is the enunciation of the Theorem as given by Prof. Loom is; as we 
consider, however, that this enunciation is incorrect and does not set out 
clearly the matter to be proven, we will give the following in its stead: The 
rate of variation of the side of a square is to the rate of variation of the cor- 
responding area, in the ratio of unity to twice the side of the unvaried square 

+ the variation of the side. Let a.b. (Fig. 1.) be 
e Figure 1. f the side of the square a, b, c, d and a, and suppose 

this side to be elongated to e in one second of time, 
b e will then be its increase and the corresponding 
increase of area will be the space b, e, f, g, d, c, b: 
let h=b e, and g=befgdcb, then h=increase of the 
side, and g=the corresponding increase of area. 
Now as h =the increase of the side in one second, 
the rate of this increase will 

h 

j be — — 

<l £ 1 

and as g = the corresponding 



b 



rate of increase will 



increase of area, its 
h a h 



be = — ; and the ratio of these rates will be = = — . 

1 1 1 g 

Now let x = ab— the side of the square abeda, and y = ae— the side of the 
square aefga; then y— x = h, and yi — x'-=g, and consequently, 



li 



10. 



y-x 



v — X 



1 

X 



y-x 



y-f-x y-f-x 



h 



g y2— x2 

But v+x— 2x-f-h. and therefore: 

11. — = . 

g 2x+h 
But as the value of g depends upon the value of h, if we make h an infini- 
tesimal (and we have seen in 2§ that the ratio of infinitesimals is the same as 
the ratio of appreciable quuatities 
we will have : 



springing from them by multiplication) 
1 



12. 



2x+0 

and hence for infinitesimal variations we have: 

h : g::l : 2x. 

Note. To treat specially of mathematics is not our object in this 

work, nor do we wish bv criticising to offer refutations: but as the under- 



35 

standing of ratio is important and as the calculus treats specially of this 
subject, to set it upon clear and true foundations must be acceptable to every 
student. And from the above demonstration it will appear to eveiy reflecting 
reader, that the ideas entertained by many teachers of the calculus, that h-7-g 
is not the true ratio of the rate of increase of the side of a square to the rate 
of increase of the corresponding area, but that in order to get at the true 
ratio we must reduce h and g to infinitesimal quantities, so That their differ- 
ence may be less than any assignable quantity, supposing that thereby the 
ratio will be the true ratio to within less than any assignable quantity, is 
erroneous. 

Again, take the Theorem: The rate of variation of the "dge of a cube 
is to the rate of variation of the corresponding solidity, in the ratio of unity 
to the square of the varied edge -+- the product of the varied and unvaried 
edges -f- the square of the unvaried edge. Let h = the variation of edge, and 
g — corresponding variation of solidity; and let y = edge of varied cube, 
and x — ede;e of unvaried cube; then 



h v-x 1 



13. 



g y3-x3 y24-y X - 



If within this equation y=x to within less than any assignable difference, 
h and g will become infinitesimals and we will have 

1 

t4. — = : 

3x2 

and hence for infinitesimal variations, h:g::l:3x2. If the edge be decreas - 
ing instead of increasing x>y and we will have 

— h x— y — h 1 

15. — = , and when x=y — = . 

— g x3 — y3 — g 3x2 

When the motion or variation of one body or thing is uniform and 
another body or thing makes commensural increments of increase or decrease 
of variation in consecutive commensural times, the latter body or thing 
varies in Arithmetrical progression; and in order to get the ratio of the 
ratios of the variations we must divide the ratio of space made by the first 
object in a given time by the ratio of the space made by the second object in 
a commensural time. Let h = space made in five minutes by an object 
making uniformly b feet per minute, and let another object move, making a 
feet for the first minute a+b for the second, a-j-2d for the third and so on for 
five minutes with the commensural increment of increase of d in each suc- 
cessive minute: 

h 
then — = ratio of the first objects variation, and letting S stand for the sum 

5 8 

of the terms in the second objects variation, — - —' ratio of second object's 

h 5 

variation and — = ratio of these ratios. But letting n = number of terms, 

S (" a-f b T 
and 1 rr last term, and h will be equal to bn, and H~ | | n, and hence: 

l a J 









h bn 2b 

15. — = = . But l=a-f-(n— l)d, and hence; 

S fa+1 ") a+1 

i In 

I 2 J 
h 2b 

16. — = , and when n=l 

S 2a-f-(n-l)d 

h b 

17. — — — ; and if we reduce h and S to infinitesimals, 

S a 

b b 
18. — = — : — , therefore, is the true ratio of the objects 1 variations 
a a 
at the infinitesimal point from which they begin to vary. 

a a 
The equation — = eives the ratio of the first term in an Arith- 

1 a+(n-l)d 
metrical progression to the last term considered. If the reader does no 
lull}' comprehend this and the following paragraphs, let him turn to some 
mathematical work upon the subjects. 

If one object vary uniformly and another object vary in such manner 
that the successive values made in com mensural times are in proportion to 
each other, i. e., the terms have a constant ratio, the latter object's variations 
are in Geometrical progression; and we find the ratio of these objects' vari- 
ations by dividing the ratio ef the one by the ratio of the other. Using the 
letters as in the preceding paragraph with the addition of r for the constant 
ratio, and relying upon the readers knowledge of mathematics we will have: 

h bn bn(r— 1) 

20. — = — ■ . But when n=l we will have 

8 arii — a a(r« — 1) 

r-1 

h b b 

21. — == — , and consequently — will be the true ratio of these 

S a a 

objects' variations at the zero point of varying. The equation 

a a 
'22. — = gives the ratio of the first term to the last term considered. 

1 aru-i 

If an object varp in Arithmetrical progression and another by Geo- 
metrical progression and we use capital letters in the Geometrical equation 
for the sum and first term we wili have 

fa+1'1 

I | * 

s I 2 J [r(a+l)-(a+b)]n 

2:5. — ^r rr • 

8 lr— A 2(lr— A) 



37 
We have gone far enough, perhaps, upon the subject of ratio. 

CHAPTER XL 

TRANSFORMATION OF PROPOSITIONS. 

If we take the three distinct propositions: 

A A A V A A A A A V A A A A A V A A 

T S T B T 8 . T8TS T S T8 TS TS 

a < b c < (1 a -=- (1 

by uniting them into one we may have 

A V A V A V 

T S T S T S 

2. 

a < < I) 

c d 

And if in proposition 2. we place the sign \ or V by the side of the terms, 
not as signs of homon or hetera, but simply as the sign of incommensura 
we will have 

A v A V A V 

T S T S T S 

Via < < b | y 
| c d I 

If we take the distinct propositions 

A A A V A A u A V A A A A A V /, A 

TS TS T S T S TS TS TS T S T S 

a < b b == c a = d 

by uniting them into one we may have 

A V A V 

T S A V T S 

5. T S . 

A ja ==< bj V 

I c d I 

And from proposition 5 by writing the sign of incommensura under the 
terms we may have the propositions 

A V A V A V A V A V A V A V 

T S A V T S TS A V TS T S T S TS 

6. TS . 7. TS . 8. . 



a-f-c == < b-fd aXc ===== < bxd a 



a — < b I V 



< > < > C d , 

If we take the commensural propositions 

A A u aa a a a a AA AA 

T S a V T S T S A V T S TS \ V TS 

9. TS , TS , TS , 

a = b c = d a == d 
by using the sign of commensura (not that of similia) by the side of the 






83 



terms we 


ma}* have 


A V 
TS 

10. 

II la 
|c 


A V AV 
T S T S 
, from wh 

" Si" 




A V A V A V 
TS TS TS 



12. 



and 13. 





A V 


A V 


A V 




TS 


TS 


TS 


/e 11. 










a-f-c 


— — ** 


b+d 


A V 


A v 


A V 




TS 


TS 


T S 





axe ===== bxd 



a r=zr: b 

c d 

If we have any number of incommensural propositions as the follow- 



ing 



AA A A 

T S a V T S 

14. TS 

a, < b 

we may derive from them 



AA 
TS 



15. 



A V 
TS 

a+d 



A A 
TS 

A < 



A V 
TS 



A V 

TS 

16. 

a+d axel 



AV 
TS 

< 



A A 
T S 



A A 
TS 



AV 
TS 



TS 



A V 

TS 

< 



AV 
TS 



A A 
TS 

, etc. 

d 



A A 
TS 



AV 
TS 



A < axd la \^ 



A 



d 



And if we have any number of incommensural propositions as the 
following : 



\ A 

T S 



18. 



AV 

TS 



A A 
TS 



A A 
TS 



a . . <: b 
we may derive from them 



A v 

TS 



AV 
TS 

< 



A A 
TS 



A A 

TS 



A A 
TS 



AV 
TS 

< 



A A 
TS 



etc. 



A V 
TS 



19. 



etc 



A < ■ a+b+c+d+e+f 






a+b+c+d+e+f 

< < < < < < 

By setting down all the signs in our transformations, we are able to integrate 
or resolve the complex propositions into their simple and primitive ones 
without any difficulty; but there is still another object of more importance 
in doing so, as we will see hereafter. 

Now we have shown heretofore, that both incommensural aud com- 
mensural propositions contain only relations inter se similia, and as we have 
used the letters a, b, c, etc., not to distinguish kinds of things, but merely to 
distinguish the quantities of similia, proposition 6 may be transformed into 



39 

20. 



A V A A a V 
T S T S T S 

a+c || || . b+ci 



< > 

And any com mensural or incommensural, or commensural incommensural, 
or incommensural commensural proposition may be transformed by striking 
out the signs of. equality and inequality between the terms and inserting in 
their stead the sign of similia. 

Now let the letters a, b, c, etc., stand for names, which distinguish 
similia and differentia and take the differential propositions 

AA AV AA AA AV AA 

TB T S T S T 8 T S T 8 

21. and — — . By uniting them we will have 

a |+ b c |+ d 

A V A V A V 

T 8 T S T S 

22. . 



a hh 14- b 
c d 

Take the propositions 

AA Ay AV A A AV a A 

TS -TS T8 TS TS T8 

23. . By uniting we will have 

a h- b a' h- b' 

VV AV AV \V AV AV 

TS TS TS T8TST8 

24. or, 25. . 

a 14- l| b a || i4- a' 

a' b' b' b 

As the letters a, b, c, etc., are distinguishing names we need not place any 
sign by the side of the terms, as we can integrate without doing so. 
Take the propositions 
Aa AV Aa A A av aa 
T8 TS T8 TS TS TS 
26. . By uniting them we have 



27. 



II a'" 

A V A V A V 

TS TS T 8 

a || |! a' 






Now we have heretofore shown that the mind's capacitv to heterate 
depends upon time and space; and it may, perhaps, be well enough to make 
a single remark further on that subject here. If a bell be struck, we can 
both see the bell and hear its sound in an homonical time, while the bell oc 
cupies an homonical space: but the organ? of vision and those of hearing 
occupy heterical spaces; and the sound and the light coming from the bell 
do not come to the mind through homonical spaces, i. e., although there be 



apparently in the case homonical time and space? 3 r et the spaces are really 
hetera, and they enable the mind to heterate. Take the heterical propositions 

A A A v A A A A A A A A 

T S T S T S T 8 T S T IS 

28. . By uniting them we will have 

a V a' b /\ b' 



29. 



But if we should transpose the terms of the first of propositions 28 and then 
unite it with itself we would have 

A.V A A A v 
T S T 8 T S 

a \ \ a 

a ' a ' 



aV 

TS 


/ v 
T S 


TS 


a 
b 


vv 


a' 
b' 



30. 



Take the propositions 

A A A A A A A A A A A A 

T 8 T 8 T S T 8 TS T8 

31. . And by uniting them we have 

a a a b a b 



32. 



A A A A 
T 8 TS T 8 



a a v a. 
b b 



But if we unite the first of the propositions 31 with itself we will have 



33. 



A A A A A A 
T S T S T S 



a a A a 
a a 



Now from the few examples given above any one with moderate 
capacity can see how to unite and transform simple propositions into com- 
plex ones and obtain all the varieties of propositions having the varieties of 
signs between the terms as set down in Chapter First ot this book and to 
place the appropriate signs over the T's and S's, we need not therefore deal 
further with this matter. 

Now we have seen in Book I, that in ever}- case of causation some 
homon is converted into hetera or vice versa; some similiaare converted into 
differentia or vice versa; or, some commensura are converted into incom- 
comensura or vice ve versa: and if we compare the simple propositions with 
the complex ones derived from them in the preceeding transformations, on 
comparison of the signs of the S's over the terms we will see, that in the 
transformations given the heteration uf space has occurred. In those trans- 
formations of propositions, however, the heteration of space may have been 
made merely by the mind ; but if we suppose a, b, c, etc., to be material 



41 

objects and t© have changed the relations in which they existed as expressed 
in the simple propositions, into the relations as expressed in the derivative 
propositions, then Causes external to the mind bringing about these changes 
have involved the heteration of space. In the transformation of simple ho- 
monical propositions into homonical homonical propositions, indeed, no 
such change in the signs of the S's is indicated, nor could the ueteration of 
space occur, were a, for instance, a material object and contemplated in its 
different mental relations. 

But in Book II we saw that among causes a homon of time and a 
homon of space are the necessary conditions of causation, and also that 
effects spring from heterical causes. Lei us suppose, therefore, a, b, c, etc., 
in the foregoing complex propositions to be causes, and let U9 make a homon 
of time and a homon of space over the terms and see what changes follow. 
If in proposition 6, we change V into /\ over the S's on the terms, we can not 
write the new proposition resulting without performing the addition ; but 
kiting y stand for the sum, we may then write the new proposition and have 



U. 



AA 


AV 


AA 


TS 


T8 


TS 



v = 



We may deal with propositions 7 and 8 in a similar manner. 

It we change V into A over the terms of proposition 11 and let v stand 
for the sum, we will have 

A A A v ' A A 
T 8 T S T 8 
85. . 

v = v 

And if in this proposition we change V into <\ between the terms we will 
have 



86; 



A A 


A A 


A A 


TS 


TS 


TS 



A 



From which changes we see, that the hotnonating of the spaces between the 
objects in the terms produces effects inter se neter*, but each of which per se 
is a homon ; and the homonating of the spaces between the terms produces 
an effect pef se homon: the converse is also true. 

If in proposition 22 we change V into A over the terms two effects 
must be produced ; and as ac and bd are differential differentia the effects 
inter se must be differentia. Let x stand for one of the effects and y for the 
other, and we will have 



37. 



AA 


AV 


A A 


TS 


TS 


TS 



H- 



And if we change V into A between the terms we will have an effect differ- 
ing from both x and y, i. e., we will have 



4* 



AA 
TS 



AA 
TS 



AA 
TS 



38. 



Let us now take propositions 23 and go through all the transforma- 
tions, which the reader will now readily understand 



AA A v 
TS TS 



*A 



a 

/ 
S 

a' 



4 A - 



H- 

AV 
TS 



H- 



s 



b 

AA 
TS 

b' 



u 


av 

TS 


av 

TS 


aV 
TS 


a 
b' 


II H- 


a' 
b 


U 


A 4 

TS 


AV 
TS 


AA 
TS 


X 


II 


X 


u 


A A 
TS 


AA 
TS 


A A 

TS 


X 


A 


X 


U 


AA 
TS 


AV 

TS 


A A 
TS 


X 


II 


X 


U 


AV 
TS 


AV 
TS 


AV 
TS 


a 
b' 


II H- 


a' 
b 



Produce by heterating space between 
objects in terms towards each other. 



By homonating space between objects 
in terms. 



By homonating space between terms. 



By heterating space between terms. 



By heterating space between objects of 
terms. 



18 



it 



AA 
TS 


A V 

TS 


A A 
TS 


a 


:i 


b 


A A 
TS 


A V 
TS 


A A 
TS 


a' 


H- 


b' 



By heterating space between objects of 
terms from each other. 



We have now gone far enough upon the subject of Transformations of 
Propositions to give the reader a thorough- understanding of the matter, it 
he will study and use his own mind in working out upon a slate the various 
transformations possible, in order to familiarize the modes of reasoning. 

CONCLUDING REMARKS. 

It was the intention of the author to have continued this book much 
further than its present limits, to treat of the ratio of gregaria and of their 
combinations ^'propositions by which what are called the laws of nature 
can be evolved, to point out errors in the fundamental principles in natural 
philosophy, to state experiments made and demonstrable results actually ob- 
tained in light, electricity and heat. But hard times, ill health, and tne great 
difficulty in getting the authors ideas in print at all, so as to place them be- 
fore the scientific world, have compelled the him to stop here; although 
the subject is abruptly broken off and much to his regret the applicability ot 
the science to the investigation ot nature is not exhibited, the author claims 
that he has made many valuable discoveries in physical science which must 
be 16ft for another work and for more auspicious circumstances, if such 
should ever come. The present edition has been put in print under the most 
harrising circumstances and difficulties, and it cannot be expected to be 
otherwise than that numerous errors and obscurities should appear in it. 
These the reader will excuse, and when scientific men shall have in- 
vestigated the work and expressed their opinion about it the author will be 
better prepared to judge of the expediency of making the attempt to com- 
plete a work on natural philosophy based upon the principles of experiment 
and reasoning exhibited in this hook. 

THE END. 





